Re: Quantum Mechanics Violation of the Second Law

[George Levy]

Thanks Bruno


On 11/11/2015 12:59 AM, Bruno Marchal wrote:

Hi George,

Congratulations!

Best wishes for you and your amazing work. I am not convinced but that 
might only be due to my incompetence in the field. I will make a 
further look.


Bruno


On 10 Nov 2015, at 23:10, George Levy wrote:

I would like to update the members of this list on what I have been 
up to recently (and revive an old thread). My latest paper "Quantum 
Game Beats Classical Odds - Thermodynamics Implications" has just 
been published by the Journal Entropy under the section "Statistical 
Mechanics" after a strict and thorough peer review. The implications 
are that it is possible to beat the laws of Classical Physics using a 
Quantum Mechanical effect. Given the right conditions it should be 
possible to produce a spontaneous temperature gradient in a 
thermoelectric material without any electrical input - and vice 
versa, to produce an electrical output without a temperature 
difference input.


Here is the link to the paper at the Journal Entropy:

http://www.mdpi.com/1099-4300/17/11/7645

I presented an earlier paper in Vancouver, Canada, which was also 
approved for publication by the /11th International Conference on 
Ceramic Materials & Components for Energy & Environmental 
Applications/. It is now undergoing editorial and format changes.


The paper is currently available at ResearchGate at

https://www.researchgate.net/publication/283645102_Anomalous_Temperature_Gradient_in_Non-Maxwellian_Gases


Best

George



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http://iridia.ulb.ac.be/~marchal/ 



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Re: Quantum Mechanics Violation of the Second Law

[Bruno Marchal]

Hi George,

Congratulations!

Best wishes for you and your amazing work. I am not convinced but that  
might only be due to my incompetence in the field. I will make a  
further look.


Bruno


On 10 Nov 2015, at 23:10, George Levy wrote:

I would like to update the members of this list on what I have been  
up to recently (and revive an old thread). My latest paper "Quantum  
Game Beats Classical Odds - Thermodynamics Implications" has just  
been published by the Journal Entropy under the section "Statistical  
Mechanics" after a strict and thorough peer review. The implications  
are that it is possible to beat the laws of Classical Physics using  
a Quantum Mechanical effect. Given the right conditions it should be  
possible to produce a spontaneous temperature gradient in a  
thermoelectric material without any electrical input - and vice  
versa, to produce an electrical output without a temperature  
difference input.


Here is the link to the paper at the Journal Entropy:

http://www.mdpi.com/1099-4300/17/11/7645

I presented an earlier paper in Vancouver, Canada, which was also  
approved for publication by the 11th International Conference on  
Ceramic Materials & Components for Energy & Environmental  
Applications. It is now undergoing editorial and format changes.


The paper is currently available at ResearchGate at

https://www.researchgate.net/publication/283645102_Anomalous_Temperature_Gradient_in_Non-Maxwellian_Gases


Best

George



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http://iridia.ulb.ac.be/~marchal/



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Re: Quantum Mechanics Violation of the Second Law

[George Levy]

I would like to update the members of this list on what I have been up 
to recently (and revive an old thread). My latest paper "Quantum Game 
Beats Classical Odds - Thermodynamics Implications" has just been 
published by the Journal Entropy under the section "Statistical 
Mechanics" after a strict and thorough peer review. The implications are 
that it is possible to beat the laws of Classical Physics using a 
Quantum Mechanical effect. Given the right conditions it should be 
possible to produce a spontaneous temperature gradient in a 
thermoelectric material without any electrical input - and vice versa, 
to produce an electrical output without a temperature difference input.


Here is the link to the paper at the Journal Entropy:

http://www.mdpi.com/1099-4300/17/11/7645

I presented an earlier paper in Vancouver, Canada, which was also 
approved for publication by the /11th International Conference on 
Ceramic Materials & Components for Energy & Environmental Applications/. 
It is now undergoing editorial and format changes.


The paper is currently available at ResearchGate at

https://www.researchgate.net/publication/283645102_Anomalous_Temperature_Gradient_in_Non-Maxwellian_Gases


Best

George


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Re: Quantum Mechanics Violation of the Second Law

[George]

Richard
you are making an interesting link. If the early universe carried a BEC 
then the stage was set for a big entropic reset. For this to occur, you 
would need a force field producing a global temperature gradient or 
multiple local gradients, and a means (i.e., heat engine) for converting 
the temperature gradient(s) into low entropy energy (i.e., work) and/or 
low temperature matter.

George

On 11/30/2014 8:36 AM, Richard Ruquist wrote:

John,

Experimental results at several high-energy colliders suggest that at 
some point in the big bang the universe was a quark-gluon plasma, 
which despite it's high energy, is a BEC where all the particles share 
the same wave function- so they say. It seems to me that if all 
particles in the universe share the same wave function, that must be a 
state of very low entropy. I invite discussion on whether my thinking 
is correct.

Richard

On Sun, Nov 30, 2014 at 11:00 AM, John Clark > wrote:


On Sat, Nov 29, 2014 at 4:29 PM, George mailto:gl...@quantics.net>> wrote:

> As I
have explained in previous posts, it is my opinion that
Loschmidt was wrong in thinking that a Maxwellian gas column
could power a perpetual motion machine of the Second kind
which would decrease in entropy in an isolated system.


Yes, Loschmidt was wrong about that.

> Loschmidt was wrong with respect to the direction of time.
In summary: entropy can decrease but time always flows forward.

Loschmidt said the link between the second law and time can
explain why entropy will be higher tomorrow than today, but it
can't explain why it was lower yesterday than today. And Loschmidt
was quite right about that, you have to take initial conditions
into consideration to explain that. In retrospect this shouldn't
have been surprising, even in a Newtonian world the laws of
physics alone are NEVER enough to figure out what a physical
system will do tomorrow or did yesterday, you also have to know
exactly what state the system was in for at least one moment in
time before yesterday. Only then can you use the laws of physics
to figure out how the system will evolve.

> His argument was that if the laws of physics are perfectly
reversible, then entropy is just as likely to increase as to
decrease.


No, it would be far worse than 50/50. His argument was that even
if the laws of physics were perfectly reversible entropy would
still almost certainly increase because there are astronomical to
the astronomical power more ways to be disorganized than
organized, so the chances are overwhelming that yesterday, the
state that produced the state that things are in today, was one of
those EXTREMELY numerous states. But nobody really thinks that
entropy decreased between yesterday and today; the thing that
saves us from this paradox is initial conditions, the universe
must have started out in a very very low entropy state and has
been winding down ever since.

  John K Clark



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Re: Quantum Mechanics Violation of the Second Law

[John Clark]

On Sun, Nov 30, 2014 at 11:36 AM, Richard Ruquist  wrote:

> Experimental results at several high-energy colliders suggest that at
> some point in the big bang the universe was a quark-gluon plasma, which
> despite it's high energy, is a BEC where all the particles share the same
> wave function- so they say. It seems to me that if all particles in the
> universe share the same wave function, that must be a state of very low
> entropy.
>

Yes, the entropy of a  Bose–Einstein Condensate would be as low as you
could get, but I hesitate to say a quark-gluon plasma is the reason the
early universe's entropy was so low; for one thing a  quark-gluon plasma is
more like a Fermion that a Boson, and for another Quarks and Gluons only
account for about 4% of the universe, 96% is Dark Matter and Dark Energy
which we know almost nothing about.

  John K Clark

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Re: Quantum Mechanics Violation of the Second Law

[Richard Ruquist]

John,

Experimental results at several high-energy colliders suggest that at some
point in the big bang the universe was a quark-gluon plasma, which despite
it's high energy, is a BEC where all the particles share the same wave
function- so they say. It seems to me that if all particles in the universe
share the same wave function, that must be a state of very low entropy. I
invite discussion on whether my thinking is correct.
Richard

On Sun, Nov 30, 2014 at 11:00 AM, John Clark  wrote:

> On Sat, Nov 29, 2014 at 4:29 PM, George  wrote:
>
>  > As I have
>> explained in previous posts, it is my opinion that Loschmidt was wrong in
>> thinking that a Maxwellian gas column could power a perpetual motion
>> machine of the Second kind which would decrease in entropy in an isolated
>> system.
>>
>
> Yes, Loschmidt was wrong about that.
>
> > Loschmidt was wrong with respect to the direction of time. In summary:
>> entropy can decrease but time always flows forward.
>>
>
> Loschmidt said the link between the second law and time can explain why
> entropy will be higher tomorrow than today, but it can't explain why it was
> lower yesterday than today. And Loschmidt was quite right about that, you
> have to take initial conditions into consideration to explain that. In
> retrospect this shouldn't have been surprising, even in a Newtonian world
> the laws of physics alone are NEVER enough to figure out what a physical
> system will do tomorrow or did yesterday, you also have to know exactly
> what state the system was in for at least one moment in time before
> yesterday. Only then can you use the laws of physics to figure out how the
> system will evolve.
>
> > His argument was that if the laws of physics are perfectly reversible,
>> then entropy is just as likely to increase as to decrease.
>>
>
> No, it would be far worse than 50/50. His argument was that even if the
> laws of physics were perfectly reversible entropy would still almost
> certainly increase because there are astronomical to the astronomical power
> more ways to be disorganized than organized, so the chances are
> overwhelming that yesterday, the state that produced the state that things
> are in today, was one of those EXTREMELY numerous states. But nobody really
> thinks that entropy decreased between yesterday and today; the thing that
> saves us from this paradox is initial conditions, the universe must have
> started out in a very very low entropy state and has been winding down ever
> since.
>
>   John K Clark
>
>
>
>
>
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Re: Quantum Mechanics Violation of the Second Law

[John Clark]

On Sat, Nov 29, 2014 at 4:29 PM, George  wrote:

 > As I have explained
> in previous posts, it is my opinion that Loschmidt was wrong in thinking
> that a Maxwellian gas column could power a perpetual motion machine of the
> Second kind which would decrease in entropy in an isolated system.
>

Yes, Loschmidt was wrong about that.

> Loschmidt was wrong with respect to the direction of time. In summary:
> entropy can decrease but time always flows forward.
>

Loschmidt said the link between the second law and time can explain why
entropy will be higher tomorrow than today, but it can't explain why it was
lower yesterday than today. And Loschmidt was quite right about that, you
have to take initial conditions into consideration to explain that. In
retrospect this shouldn't have been surprising, even in a Newtonian world
the laws of physics alone are NEVER enough to figure out what a physical
system will do tomorrow or did yesterday, you also have to know exactly
what state the system was in for at least one moment in time before
yesterday. Only then can you use the laws of physics to figure out how the
system will evolve.

> His argument was that if the laws of physics are perfectly reversible,
> then entropy is just as likely to increase as to decrease.
>

No, it would be far worse than 50/50. His argument was that even if the
laws of physics were perfectly reversible entropy would still almost
certainly increase because there are astronomical to the astronomical power
more ways to be disorganized than organized, so the chances are
overwhelming that yesterday, the state that produced the state that things
are in today, was one of those EXTREMELY numerous states. But nobody really
thinks that entropy decreased between yesterday and today; the thing that
saves us from this paradox is initial conditions, the universe must have
started out in a very very low entropy state and has been winding down ever
since.

  John K Clark

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Re: Quantum Mechanics Violation of the Second Law

[George]

Hi Russel, Liz

Please feel free to forward these emails to people who may shed some 
light on this issue. As I mentioned I consider myself more a student 
than an expert and I welcome anyone who could either prove or disprove 
these ideas.


Russell, from your previous post you appear to be one of the most 
knowledgeable in Thermodynamics in this list. Yet your response, 
_guessing_ that the Second Law is not actually broken but _not knowing 
why_, is typical of many scientists_including myself three years ago 
before I began this study_.


The question I am raising is difficult. Again, feel free to forward 
these emails to knowledgeable people.


Liz,  you are raising two questions:
1) Does the Second Law survive?
2)  Linking the Arrow of time with entropy.

1) Does the Second Law survive?
There are many Second Laws : Heat flows from hot to cold (Clausius), 
Entropy must always increase (Boltzmann), Perpetual Motion Machines of 
the 2nd kind do not exist (Kelvin)
In my view, the most general formulation of the Second Law is the 
Fundamental Postulate of Thermodynamics which states that the 
microstates of an isolated system are equiprobable.
more info at 
http://en.wikipedia.org/wiki/Statistical_mechanics#Fundamental_postulate


This formulation will survive as it is a basis for the derivation of the 
Fermi-Dirac, the Bose-Einstein and of course the Maxwell-Boltzmann 
statistics.


2)  Linking the Arrow of time with entropy.
Loschmidt issued (at least) two Second Law challenges. In his first one 
he argued that a perpetual motion machine of the second kind could 
exploit the temperature differential in a gas column, thereby causing 
entropy to decrease. See: 
http://link.springer.com/book/10.1007/1-4020-3016-9
His second challenge has to do with the irreversibility of time. His 
argument was that if the laws of physics are perfectly reversible, then 
entropy is just as likely to increase as to decrease. See 
http://en.wikipedia.org/wiki/Loschmidt%27s_paradox


As I have explained in previous posts, it is my opinion that Loschmidt 
was wrong in thinking that a Maxwellian gas column could power a 
perpetual motion machine of the Second kind which would decrease in 
entropy in an isolated system. However, such a machine could still be 
built if one uses a non-Maxwellian gas. So Loschmidt was right in 
thinking that entropy could be made to decrease.


Does that mean that time can flow backward? The answer is no. If one 
were to build such a machine, the direction of heat flow would be 
irreversible and easily identifiable. Heat would flow from cold to hot 
in the Fermi-Dirac gas and from hot to cold in the classical portion of 
the machine.  Time would not flow backward. There is a lot of literature 
on this topic but from the narrow point of view of a non-Maxwellian 
perpetual motion machine, Loschmidt was wrong with respect to the 
direction of time.


In summary: entropy can decrease but time always flows forward.

Best,
George Levy




On 11/28/2014 3:14 PM, Russell Standish wrote:

I'm with Liz - I suspect that George is using a specific version of
entropy that is (say) only applicable for canonical or microcanonical
ensembles, and that the second law actually survives because the system is in
neither ensemble.

But I could be wrong - its been far too many years since I studied
such basic statistical mechanics, and I don't have the time nor energy
to revisit the topic now :(.

Cheers

On Sat, Nov 29, 2014 at 11:15:18AM +1300, LizR wrote:

Is this a violation of the 2nd law, or is it an outcome of the 2nd law that
doesn't take the expected form? (I would expect a violation of the law to
involve something anti-entropic going on, which would look to us like time
running backwards).

On 29 November 2014 at 10:48, George  wrote:


  Thank you Liz, Bruce and John for your comments. I am grateful that you
are forcing me to explain myself in simple terms, and this is exactly what
I need to do. I am definitely not an expert in this field. I consider
myself more like a student and I am eager for constructive and informed
feedback.

As John pointed out, the Second Law is not like the other laws of Physics.
It is more like a law of Logic or Mathematics. It appears to be as
inevitable as the value of Pi ... until you realize that Pi is tied to a
flat plane. And breaking the Second Law when certain conditions are met is
not so bad. In fact it make the universe more interesting, not less
interesting as John suggested.

Maxwell-Boltzmann's distribution is closely associated with the Second
Law. Let me try to explain in very simple terms how this distribution is
obtained.

Starting with the *uniform* distribution (microstates are evenly
distributed in phase space) one can show that the velocity distribution of
gas molecules along any one degree of freedom, is *Normal*. i.e., the
mean velocity vx (or vy or vz) is 0 and the standard deviation is a
function of temperature.

 From this, one can show that the Velocity 

Re: Quantum Mechanics Violation of the Second Law

[Russell Standish]

I'm with Liz - I suspect that George is using a specific version of
entropy that is (say) only applicable for canonical or microcanonical
ensembles, and that the second law actually survives because the system is in
neither ensemble.

But I could be wrong - its been far too many years since I studied
such basic statistical mechanics, and I don't have the time nor energy
to revisit the topic now :(.

Cheers

On Sat, Nov 29, 2014 at 11:15:18AM +1300, LizR wrote:
> Is this a violation of the 2nd law, or is it an outcome of the 2nd law that
> doesn't take the expected form? (I would expect a violation of the law to
> involve something anti-entropic going on, which would look to us like time
> running backwards).
> 
> On 29 November 2014 at 10:48, George  wrote:
> 
> >  Thank you Liz, Bruce and John for your comments. I am grateful that you
> > are forcing me to explain myself in simple terms, and this is exactly what
> > I need to do. I am definitely not an expert in this field. I consider
> > myself more like a student and I am eager for constructive and informed
> > feedback.
> >
> > As John pointed out, the Second Law is not like the other laws of Physics.
> > It is more like a law of Logic or Mathematics. It appears to be as
> > inevitable as the value of Pi ... until you realize that Pi is tied to a
> > flat plane. And breaking the Second Law when certain conditions are met is
> > not so bad. In fact it make the universe more interesting, not less
> > interesting as John suggested.
> >
> > Maxwell-Boltzmann's distribution is closely associated with the Second
> > Law. Let me try to explain in very simple terms how this distribution is
> > obtained.
> >
> > Starting with the *uniform* distribution (microstates are evenly
> > distributed in phase space) one can show that the velocity distribution of
> > gas molecules along any one degree of freedom, is *Normal*. i.e., the
> > mean velocity vx (or vy or vz) is 0 and the standard deviation is a
> > function of temperature.
> >
> > From this, one can show that the Velocity = Sqrt(vx^2+vy^2+vz^2) is
> > Chi-Square and that Energy follows Maxwell's distribution. You can look up
> > details about Maxwell at
> > http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution.
> >
> > Boltzmann modified Maxwell's distribution (to produce the
> > Maxwell-Boltzmann distribution) by adding an exponential factor i.e.,
> > Maxwell * exp(E/kT)   where E = potential energy, to account for the
> > potential energy that gas molecules acquire when they rise in a
> > gravitational field. The Boltzmann factor varies with altitude because the
> > potential energy E varies.
> >
> > This brings us to why Loschmidt was wrong in suggesting that energy can be
> > extracted from a Maxwellian gas in a gravitational field.   Density also
> > varies with altitude and the Boltzmann factor disappears when the
> > distribution is renormalized to account for the change in density. In other
> > words the Maxwellian term remains constant with altitude. This means that
> > the temperature is constant with altitude.
> >
> > Hence a Maxwellian gas complies with the Second Law. Continuing the
> > analogy, Pi = 3.14159 the plane is flat. Physics is Classical and
> > Geometry is Euclidean.
> >
> > Fermions follow the Pauli Exclusion Principle which makes their statistics
> > non-Maxwellian. The term describing potential energy is embedded in the
> > Fermi-Dirac formula. It is not added as a simple factor. See
> > http://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics
> > Going through the exercise of renormalization, one discovers that Fermion
> > temperature is not constant with altitude. The analogy is Pi=/= 3.14159,
> > the surface is curved and Physics is Quantum.
> >
> > This reasoning also applies to Bosons which follow Bose-Einstein
> > statistics.
> >
> > Experimental data on thermoelectric materials obtained at Caltech and
> > extensive simulations by myself and others have confirmed the above.
> >
> > This is a complex topic and I welcome the assistance of experts in the
> > field of Quantum Thermodynamics to either confirm or disprove these ideas.
> > Please do not hesitate to forward this email to anyone who you think might
> > provide enlightenment.
> >
> > Best
> >
> > George Levy
> >
> >
> >
> >
> >
> >
> > On 11/27/2014 6:33 PM, John Clark wrote:
> >
> > On Thu, Nov 27, 2014 at 7:09 PM, Bruce Kellett 
> > wrote:
> >
> >   >> The 2nd law is like that - unlikely things generally failing to
> >>> happen - on the molecular scale, a zillion times per second. You can't
> >>> circumvent it unless you can circumvent the maths of probability.
> >>>
> >>
> >>  > Which means that it counts as a law of physics.
> >
> >
> >  The second law is more fundamental than merely a law of physics. I can
> > imagine some particular universe in the multiverse where the conservation
> > of energy did not hold, according to Norther's theorem a universe where
> > physics changed as a function of 

Re: Quantum Mechanics Violation of the Second Law

[LizR]

Is this a violation of the 2nd law, or is it an outcome of the 2nd law that
doesn't take the expected form? (I would expect a violation of the law to
involve something anti-entropic going on, which would look to us like time
running backwards).

On 29 November 2014 at 10:48, George  wrote:

>  Thank you Liz, Bruce and John for your comments. I am grateful that you
> are forcing me to explain myself in simple terms, and this is exactly what
> I need to do. I am definitely not an expert in this field. I consider
> myself more like a student and I am eager for constructive and informed
> feedback.
>
> As John pointed out, the Second Law is not like the other laws of Physics.
> It is more like a law of Logic or Mathematics. It appears to be as
> inevitable as the value of Pi ... until you realize that Pi is tied to a
> flat plane. And breaking the Second Law when certain conditions are met is
> not so bad. In fact it make the universe more interesting, not less
> interesting as John suggested.
>
> Maxwell-Boltzmann's distribution is closely associated with the Second
> Law. Let me try to explain in very simple terms how this distribution is
> obtained.
>
> Starting with the *uniform* distribution (microstates are evenly
> distributed in phase space) one can show that the velocity distribution of
> gas molecules along any one degree of freedom, is *Normal*. i.e., the
> mean velocity vx (or vy or vz) is 0 and the standard deviation is a
> function of temperature.
>
> From this, one can show that the Velocity = Sqrt(vx^2+vy^2+vz^2) is
> Chi-Square and that Energy follows Maxwell's distribution. You can look up
> details about Maxwell at
> http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution.
>
> Boltzmann modified Maxwell's distribution (to produce the
> Maxwell-Boltzmann distribution) by adding an exponential factor i.e.,
> Maxwell * exp(E/kT)   where E = potential energy, to account for the
> potential energy that gas molecules acquire when they rise in a
> gravitational field. The Boltzmann factor varies with altitude because the
> potential energy E varies.
>
> This brings us to why Loschmidt was wrong in suggesting that energy can be
> extracted from a Maxwellian gas in a gravitational field.   Density also
> varies with altitude and the Boltzmann factor disappears when the
> distribution is renormalized to account for the change in density. In other
> words the Maxwellian term remains constant with altitude. This means that
> the temperature is constant with altitude.
>
> Hence a Maxwellian gas complies with the Second Law. Continuing the
> analogy, Pi = 3.14159 the plane is flat. Physics is Classical and
> Geometry is Euclidean.
>
> Fermions follow the Pauli Exclusion Principle which makes their statistics
> non-Maxwellian. The term describing potential energy is embedded in the
> Fermi-Dirac formula. It is not added as a simple factor. See
> http://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics
> Going through the exercise of renormalization, one discovers that Fermion
> temperature is not constant with altitude. The analogy is Pi=/= 3.14159,
> the surface is curved and Physics is Quantum.
>
> This reasoning also applies to Bosons which follow Bose-Einstein
> statistics.
>
> Experimental data on thermoelectric materials obtained at Caltech and
> extensive simulations by myself and others have confirmed the above.
>
> This is a complex topic and I welcome the assistance of experts in the
> field of Quantum Thermodynamics to either confirm or disprove these ideas.
> Please do not hesitate to forward this email to anyone who you think might
> provide enlightenment.
>
> Best
>
> George Levy
>
>
>
>
>
>
> On 11/27/2014 6:33 PM, John Clark wrote:
>
> On Thu, Nov 27, 2014 at 7:09 PM, Bruce Kellett 
> wrote:
>
>   >> The 2nd law is like that - unlikely things generally failing to
>>> happen - on the molecular scale, a zillion times per second. You can't
>>> circumvent it unless you can circumvent the maths of probability.
>>>
>>
>>  > Which means that it counts as a law of physics.
>
>
>  The second law is more fundamental than merely a law of physics. I can
> imagine some particular universe in the multiverse where the conservation
> of energy did not hold, according to Norther's theorem a universe where
> physics changed as a function of time would be like that; and I can imagine
> some universe in the multiverse where the conservation of momentum did not
> hold, a universe where physics changed as a function of space would be like
> that. But the only universe where the 2nd law didn't hold would be a
> universe of infinite boredom that consisted of nothing but white noise.
>
>John K Clark
>
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Re: Quantum Mechanics Violation of the Second Law

[George]

Thank you Liz, Bruce and John for your comments. I am grateful that you 
are forcing me to explain myself in simple terms, and this is exactly 
what I need to do. I am definitely not an expert in this field. I 
consider myself more like a student and I am eager for constructive and 
informed feedback.


As John pointed out, the Second Law is not like the other laws of 
Physics. It is more like a law of Logic or Mathematics. It appears to be 
as inevitable as the value of Pi ... until you realize that Pi is tied 
to a flat plane. And breaking the Second Law when certain conditions are 
met is not so bad. In fact it make the universe more interesting, not 
less interesting as John suggested.


Maxwell-Boltzmann's distribution is closely associated with the Second 
Law. Let me try to explain in very simple terms how this distribution is 
obtained.


Starting with the _uniform_ distribution (microstates are evenly 
distributed in phase space) one can show that the velocity distribution 
of gas molecules along any one degree of freedom, is _Normal_. i.e., the 
mean velocity vx (or vy or vz) is 0 and the standard deviation is a 
function of temperature.


From this, one can show that the Velocity = Sqrt(vx^2+vy^2+vz^2) is 
Chi-Square and that Energy follows Maxwell's distribution. You can look 
up details about Maxwell at 
http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution.


Boltzmann modified Maxwell's distribution (to produce the 
Maxwell-Boltzmann distribution) by adding an exponential factor i.e., 
Maxwell * exp(E/kT)   where E = potential energy, to account for the 
potential energy that gas molecules acquire when they rise in a 
gravitational field. The Boltzmann factor varies with altitude because 
the potential energy E varies.


This brings us to why Loschmidt was wrong in suggesting that energy can 
be extracted from a Maxwellian gas in a gravitational field.   Density 
also varies with altitude and the Boltzmann factor disappears when the 
distribution is renormalized to account for the change in density. In 
other words the Maxwellian term remains constant with altitude. This 
means that the temperature is constant with altitude.


Hence a Maxwellian gas complies with the Second Law. Continuing the 
analogy, Pi = 3.14159 the plane is flat. Physics is Classical and 
Geometry is Euclidean.


Fermions follow the Pauli Exclusion Principle which makes their 
statistics non-Maxwellian. The term describing potential energy is 
embedded in the Fermi-Dirac formula. It is not added as a simple factor. See

http://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics
Going through the exercise of renormalization, one discovers that 
Fermion temperature is not constant with altitude. The analogy is Pi=/= 
3.14159, the surface is curved and Physics is Quantum.


This reasoning also applies to Bosons which follow Bose-Einstein statistics.

Experimental data on thermoelectric materials obtained at Caltech and 
extensive simulations by myself and others have confirmed the above.


This is a complex topic and I welcome the assistance of experts in the 
field of Quantum Thermodynamics to either confirm or disprove these 
ideas.  Please do not hesitate to forward this email to anyone who you 
think might provide enlightenment.


Best

George Levy





On 11/27/2014 6:33 PM, John Clark wrote:
On Thu, Nov 27, 2014 at 7:09 PM, Bruce Kellett 
mailto:bhkell...@optusnet.com.au>> wrote:


>> The 2nd law is like that - unlikely things generally
failing to happen - on the molecular scale, a zillion times
per second. You can't circumvent it unless you can circumvent
the maths of probability.


> Which means that it counts as a law of physics. 



The second law is more fundamental than merely a law of physics. I can 
imagine some particular universe in the multiverse where the 
conservation of energy did not hold, according to Norther's theorem a 
universe where physics changed as a function of time would be like 
that; and I can imagine some universe in the multiverse where the 
conservation of momentum did not hold, a universe where physics 
changed as a function of space would be like that. But the only 
universe where the 2nd law didn't hold would be a universe of infinite 
boredom that consisted of nothing but white noise.


  John K Clark

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Re: Quantum Mechanics Violation of the Second Law

[John Clark]

On Thu, Nov 27, 2014 at 7:09 PM, Bruce Kellett 
wrote:

>> The 2nd law is like that - unlikely things generally failing to happen -
>> on the molecular scale, a zillion times per second. You can't circumvent it
>> unless you can circumvent the maths of probability.
>>
>
> > Which means that it counts as a law of physics.


The second law is more fundamental than merely a law of physics. I can
imagine some particular universe in the multiverse where the conservation
of energy did not hold, according to Norther's theorem a universe where
physics changed as a function of time would be like that; and I can imagine
some universe in the multiverse where the conservation of momentum did not
hold, a universe where physics changed as a function of space would be like
that. But the only universe where the 2nd law didn't hold would be a
universe of infinite boredom that consisted of nothing but white noise.

  John K Clark

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Re: Quantum Mechanics Violation of the Second Law

[Bruce Kellett]

LizR wrote:
I don't understand how this works, so I can't comment on the details. I 
seem to remember asking for a simple version that a dummy like me can 
understand - and don't recall seeing it, although maybe I missed it.


But in any case the 2nd law isn't a law of physics, it's just what tends 
to happen given certain circumstances. Say you lose one earring, what 
are the chances someone will find it, recognised it as yours and mail it 
to you? Generally rather low, but it could happen, it just relies on an 
unlikely chain of random factors operating in your favour, to quote Mr 
Spock.


The 2nd law is like that - unlikely things generally failing to happen - 
on the molecular scale, a zillion times per second. You can't circumvent 
it unless you can circumvent the maths of probability.


Which means that it counts as a law of physics. You seem to want to 
impose some higher standard of law-likeness on Thermodynamics. 
Probabilistic laws are perfectly law-like -- just think quantum mechanics.


Bruce

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Re: Quantum Mechanics Violation of the Second Law

[LizR]

I don't understand how this works, so I can't comment on the details. I
seem to remember asking for a simple version that a dummy like me can
understand - and don't recall seeing it, although maybe I missed it.

But in any case the 2nd law isn't a law of physics, it's just what tends to
happen given certain circumstances. Say you lose one earring, what are the
chances someone will find it, recognised it as yours and mail it to you?
Generally rather low, but it could happen, it just relies on an unlikely
chain of random factors operating in your favour, to quote Mr Spock.

The 2nd law is like that - unlikely things generally failing to happen - on
the molecular scale, a zillion times per second. You can't circumvent it
unless you can circumvent the maths of probability.

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Re: Quantum Mechanics Violation of the Second Law

[George]

Hi everyone

Not much of a response...
answering the two questions below:

Answer to question 1: If air is forcefully convected in a column having 
an isothermal temperature gradient, the column shifts toward an 
adiabatic gradient. Paradoxically, mixing does not equalize temperature, 
as is well known in meteorology. (air rising over a mountain gets colder)


Answer to Question 2: After the fans are turned off  and the air 
currents die down, the column slowly shifts back to its original 
isothermal state by diffusive heat flow. Loschmidt conjectured that the 
adiabatic state is inherently stable and that the column would remain in 
an adiabatic state. He was wrong with respect to gases such as air which 
have a mostly Maxwell-Boltzmann distribution. Gravity needs to be 
accounted for by multiplying the distribution by an exponential 
Boltzmann factor. This factor is eliminated by renormalization and the 
original distribution is recovered indicated no change in temperature.


Non-Maxwellian gases such as electrical carriers in a thermoelectric 
material follow the Fermi-Dirac distribution. This distribution does not 
allow the electrical field to be accounted for by means of a simple 
multiplicative Boltzmann factor that can be eliminated by 
renormalization.  Therefore, the carriers can acquire a temperature 
gradient when subjected to an electrical field as shown by the Caltech 
experiments and numerous simulations by myself and others.


In my opinion, the Second Law is built in, but can be circumvented by 
stepping outside of, classical physics.


George Levy

On 11/24/2014 12:24 PM, George wrote:


The gas does not flow unidirectionally in the column as in a pipe. 
There is no net flow. Convection involves a cyclic, mostly vertical, 
movement of gas in the column.


Here is a thought experiment you may consider. A column of gas in a 
gravitational field is initially assigned an isothermal temperature 
distribution. Fans are placed at the bottom and configured to blow air 
vertically, setting up a forced convection.

Question 1: Will the column remain isothermal?
Question 2: What happens if the fans are turned off. What will the 
column final state be?
These are tricky questions but answering them may enlighten the 
Loschmidt paradox.

George Levy


On 11/23/2014 5:38 PM, John Clark wrote:
On Sun, Nov 23, 2014 at 6:28 PM, George > wrote:


> There is no convection current even though gas near the floor
is hotter than gas near the ceiling. The reason is that gas
rising in an adiabatic column expands and cools exactly at the
same rate as the adiabatic temperature lapse and therefore the
gas is in equilibrium.


But what if the column of gas can't expand because it's in a sealed 
insulated pipe?


> Loschmidt ignored the fact that the energy of the molecules is
correlated with their vertical direction of movement. For
example, those molecules which are at the top of their
trajectories (zero vertical kinetic energy) must always
experience their next collision at a lower elevation.


But there will always be some molecules at the very top of the 
column, does that mean there will always be a downward current 
starting from the very top and a corresponding upward replacement 
current? Obviously do to the second law we know you couldn't set up a 
turbine and get work out of one of those currents, but exactly where 
is the flaw in the idea?  Perhaps the error is that the 2 currents 
would be so small and intermingled that the turbine would just move 
back and forth in a random way and so you couldn't get any work out 
of it, and connecting the turbine to a ratchet wouldn't help because 
the ratchet is at the same temperature as the gas so it will undergo 
Brownian motion, and the bouncing ratchet teeth will slip at random 
intervals and allow the ratchet to slip backwards, so the end result 
is no net work.


  John K Clark









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Re: Quantum Mechanics Violation of the Second Law

[George]

The gas does not flow unidirectionally in the column as in a pipe. There 
is no net flow. Convection involves a cyclic, mostly vertical, movement 
of gas in the column.


Here is a thought experiment you may consider. A column of gas in a 
gravitational field is initially assigned an isothermal temperature 
distribution. Fans are placed at the bottom and configured to blow air 
vertically, setting up a forced convection.

Question 1: Will the column remain isothermal?
Question 2: What happens if the fans are turned off. What will the 
column final state be?
These are tricky questions but answering them may enlighten the 
Loschmidt paradox.

George Levy


On 11/23/2014 5:38 PM, John Clark wrote:
On Sun, Nov 23, 2014 at 6:28 PM, George > wrote:


> There is no convection current even though gas near the floor is
hotter than gas near the ceiling. The reason is that gas rising in
an adiabatic column expands and cools exactly at the same rate as
the adiabatic temperature lapse and therefore the gas is in
equilibrium.


But what if the column of gas can't expand because it's in a sealed 
insulated pipe?


> Loschmidt ignored the fact that the energy of the molecules is
correlated with their vertical direction of movement. For example,
those molecules which are at the top of their trajectories (zero
vertical kinetic energy) must always experience their next
collision at a lower elevation.


But there will always be some molecules at the very top of the column, 
does that mean there will always be a downward current starting from 
the very top and a corresponding upward replacement current? Obviously 
do to the second law we know you couldn't set up a turbine and get 
work out of one of those currents, but exactly where is the flaw in 
the idea?  Perhaps the error is that the 2 currents would be so small 
and intermingled that the turbine would just move back and forth in a 
random way and so you couldn't get any work out of it, and connecting 
the turbine to a ratchet wouldn't help because the ratchet is at the 
same temperature as the gas so it will undergo Brownian motion, and 
the bouncing ratchet teeth will slip at random intervals and allow the 
ratchet to slip backwards, so the end result is no net work.


  John K Clark









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Re: Quantum Mechanics Violation of the Second Law

[John Clark]

On Sun, Nov 23, 2014 at 6:28 PM, George  wrote:

> There is no convection current even though gas near the floor is hotter
> than gas near the ceiling. The reason is that gas rising in an adiabatic
> column expands and cools exactly at the same rate as the adiabatic
> temperature lapse and therefore the gas is in equilibrium.
>

But what if the column of gas can't expand because it's in a sealed
insulated pipe?

> Loschmidt ignored the fact that the energy of the molecules is correlated
> with their vertical direction of movement. For example, those molecules
> which are at the top of their trajectories (zero vertical kinetic energy)
> must always experience their next collision at a lower elevation.
>

But there will always be some molecules at the very top of the column, does
that mean there will always be a downward current starting from the very
top and a corresponding upward replacement current? Obviously do to the
second law we know you couldn't set up a turbine and get work out of one of
those currents, but exactly where is the flaw in the idea?  Perhaps the
error is that the 2 currents would be so small and intermingled that the
turbine would just move back and forth in a random way and so you couldn't
get any work out of it, and connecting the turbine to a ratchet wouldn't
help because the ratchet is at the same temperature as the gas so it will
undergo Brownian motion, and the bouncing ratchet teeth will slip at random
intervals and allow the ratchet to slip backwards, so the end result is no
net work.

  John K Clark

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Re: Quantum Mechanics Violation of the Second Law

[Bruce Kellett]

George wrote:



Thanks Bruno, Bruce, Brent, Liz, John for your responses.

1)  Regarding convection currents in a gas column with an adiabatic 
temperature profile. There is no convection current even though gas near 
the floor is hotter than gas near the ceiling. The reason is that gas 
rising in an adiabatic column expands and cools exactly at the same rate 
as the adiabatic temperature lapse and therefore the gas is in 
equilibrium. All gradients ranging from isothermal to adiabatic cannot 
support convection. To get convection one needs a gradient steeper than 
the adiabatic gradient. This point is well understood by meteorologists. 
It should be made clearer in physics classes.


I think there is a difference between having a column of gas at thermal 
equilibrium absent an external field (gravitational or other) and the 
stable situation in a gravitational field. I think the stable situation 
in the field is such that the temperature is uniform throughout (so 
there is no convection as there could be in a transitional state when 
some filed is turned on). The thing to remember is that the pressure of 
the gas varies with height -- lower levels are at a higher pressure to 
support the mass of gas above. Pressure can be increased either by 
raising the temperature or by raising the density. I think the stable 
situation  for the column of gas in a gravity field is for a constant 
temperature but a density gradient.




2)  Regarding Liz’s comment regarding the Second Law and gravity. 
Yes, the Second Law is linked to gravity (and to other forces as well). 
See the paper by Erik Verlinde “On the Origin of Gravity and the Laws of 
Newton” at http://arxiv.org/abs/1001.0785.  The violation that I am 
discussing is at the intersection of gravity and QM.


Verlinde's ideas about 'entropic gravity' caused a short-lived stir in 
some circles, but the idea didn't really lead anywhere and is now 
somewhat out of favour.




3)  Regarding why Loschmidt was wrong. Brent is the one who got 
closest to the answer. 
Loschmidt ignored the fact that the energy of the molecules is 
correlated with their vertical direction of movement. For example, those 
molecules which are at the top of their trajectories (zero vertical 
kinetic energy) must always experience their next collision at a lower 
elevation. In general the smaller the kinetic energy of a molecule, the 
more likely it is to experience its next collision at a lower elevation. 
Gravity operates as an energy separator shifting upward molecules with 
higher total energy. This effect exactly counterbalances the effect 
Loschmidt was relying on that (i.e., molecules get cooler as they rise 
against gravity). The gas column remains isothermal.


This analysis seems a little one-dimensional to me. Although the 
potential is in one dimension, at any particular height in the column 
collisions in the transverse directions are going to cause rapid 
thermalization at that level. In other words, the increase in vertical 
momentum for a falling molecule is rapidly distributed over the 
transverse directions as well. In the transitional phase, molecules are 
going to sink on average because the pressure must be higher at lower 
levels. The steady state is, as I have claimed, a density gradient at a 
uniform temperature throughout.


Bruce






A more formal approach is to utilize molecular distributions. For a 
Maxwell gas subjected to an energy gradient   the energy distribution is


  

If the molecules are subjected to a potential energy  , a Boltzmann 
factor  needs to be added and the above equation becomes





The red curve shows the distribution with V = 0 (ground) and the blue 
curve with V>0. Notice the lowering in the density.


The renormalized equation is given by



(notice that renormalization eliminated the V term because it is 
expressed in an exponent and can be seen as a constant factor )


The resulting curve at elevation > ground is identical to the original


**

 

This shows that Loschmidt was wrong. A column of gas following Maxwell’s 
distribution cannot spontaneously develop a temperature gradient. It 
remains isothermal.


 


Best

George Levy


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Re: Quantum Mechanics Violation of the Second Law

[George]

Thanks Bruno, Bruce, Brent, Liz, John for your responses.

1)Regarding convection currents in a gas column with an adiabatic 
temperature profile. There is no convection current even though gas near 
the floor is hotter than gas near the ceiling. The reason is that gas 
rising in an adiabatic column expands and cools exactly at the same rate 
as the adiabatic temperature lapse and therefore the gas is in 
equilibrium. All gradients ranging from isothermal to adiabatic cannot 
support convection. To get convection one needs a gradient steeper than 
the adiabatic gradient. This point is well understood by meteorologists. 
It should be made clearer in physics classes.


2)Regarding Liz’s comment regarding the Second Law and gravity. Yes, the 
Second Law is linked to gravity (and to other forces as well). See the 
paper by Erik Verlinde “On the Origin of Gravity and the Laws of Newton” 
at http://arxiv.org/abs/1001.0785.The violation that I am discussing is 
at the intersection of gravity and QM.


3)Regarding why Loschmidt was wrong. Brent is the one who got closest to 
the answer.
Loschmidt ignored the fact that the energy of the molecules is 
correlated with their vertical direction of movement. For example, those 
molecules which are at the top of their trajectories (zero vertical 
kinetic energy) must always experience their next collision at a lower 
elevation. In general the smaller the kinetic energy of a molecule, the 
more likely it is to experience its next collision at a lower elevation. 
Gravity operates as an energy separator shifting upward molecules with 
higher total energy. This effect exactly counterbalances the effect 
Loschmidt was relying on that (i.e., molecules get cooler as they rise 
against gravity). The gas column remains isothermal.


A more formal approach is to utilize molecular distributions. For a 
Maxwell gas subjected to an energy gradient the energy distribution is


If the molecules are subjected to a potential energy , a Boltzmann 
factor needs to be added and the above equation becomes





The red curve shows the distribution with V = 0 (ground) and the blue 
curve with V>0. Notice the lowering in the density.


The renormalized equation is given by



(notice that renormalization eliminated the V term because it is 
expressed in an exponent and can be seen as a constant factor )


The resulting curve at elevation > ground is identical to the original


**

This shows that Loschmidt was wrong. A column of gas following Maxwell’s 
distribution cannot spontaneously develop a temperature gradient. It 
remains isothermal.


Best

George Levy



On 11/23/2014 8:39 AM, John Clark wrote:


On Sat, Nov 22, 2014 at 11:48 PM, Bruce Kellett 
mailto:bhkell...@optusnet.com.au>> wrote:


> I think the answer probably lies in the fact that the situation
described is not stable -- the system is not in thermal
equilibrium. As stated, the gas at the top of the column tends to
be cooler because of the higher gravitational potential. But
again, as Brent points out, the warmer gas at the bottom tends to
rise, so convection currents act to counter the gravitational
potential difference. 



Could I use those convection currents to turn a windmill that powers a 
electric generator and get work out of it?


> the system never reaches a stable equilibrium.


Does that mean that the convection currents and my generator will 
never stop? Obviously not although I confess it's not immediately 
clear to me why not.


 John K Clark



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Re: Quantum Mechanics Violation of the Second Law

[John Clark]

On Sat, Nov 22, 2014 at 11:48 PM, Bruce Kellett 
wrote:

> I think the answer probably lies in the fact that the situation described
> is not stable -- the system is not in thermal equilibrium. As stated, the
> gas at the top of the column tends to be cooler because of the higher
> gravitational potential. But again, as Brent points out, the warmer gas at
> the bottom tends to rise, so convection currents act to counter the
> gravitational potential difference.


Could I use those convection currents to turn a windmill that powers a
electric generator and get work out of it?


> > the system never reaches a stable equilibrium.
>

Does that mean that the convection currents and my generator will never
stop? Obviously not although I confess it's not immediately clear to me why
not.

 John K Clark

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Re: Quantum Mechanics Violation of the Second Law

[Bruce Kellett]

meekerdb wrote:

On 11/22/2014 10:07 PM, Bruce Kellett wrote:

meekerdb wrote:

On 11/22/2014 8:48 PM, Bruce Kellett wrote:

John Clark wrote:
On Sat, Nov 22, 2014 , meekerdb > wrote:


 > Loschmidt's idea was that an isolated column of gas in a
gravitational field would develop a temperature gradient, 
warmer at

the top.

I believe that would be cooler at the top not warmer,. molecules at 
the top of a column of gas would have more gravitational potential 
energy than those at the bottom and so would have had to expend 
kinetic energy to get up that high and become cooler as a result. 
Virtually everybody agrees that this is not in violation of the 
second law but there doesn't seem to be a consensus on exactly why 
it doesn't.


I think the answer probably lies in the fact that the situation 
described is not stable -- the system is not in thermal equilibrium. 
As stated, the gas at the top of the column tends to be cooler 
because of the higher gravitational potential. But again, as Brent 
points out, the warmer gas at the bottom tends to rise, so 
convection currents act to counter the gravitational potential 
difference. Differences in density give rise to convection. If there 
is no heat transfer to or from the outside, the system never reaches 
a stable equilibrium.


If there were always convection currents then mechanical energy could 
be extracted from the motion instead of from the temperature gradient.


Would it be that stable? Or would you just be in a Maxwell Demon 
situation. Detecting the convection currents would destroy them, so 
you couldn't actually extract useful work.


Naah, convection currents are plenty macroscopic and detectable. But 
again I'm not clear on how this is supposed to violate the second law.  
I guess it's that the isolated column supposedly gets colder as energy 
is extracted so its thermodynamic entropy goes down and the extracted 
mechanical energy has zero entropy, so the net entropy is decreased.  
But that's neglecting the gravitation. Gravitating systems have negative 
specific heat, so whenever you extract mechanical energy their 
temperature goes up.


You are probably right. Extracting energy from this system makes the 
column of gas contract, so it warms up. This is what would happen if the 
sun were powered by gravitational contraction only, and no-one suggests 
that such a process would violate the second law.


Bruce

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Re: Quantum Mechanics Violation of the Second Law

[meekerdb]

On 11/22/2014 10:07 PM, Bruce Kellett wrote:

meekerdb wrote:

On 11/22/2014 8:48 PM, Bruce Kellett wrote:

John Clark wrote:
On Sat, Nov 22, 2014 , meekerdb mailto:meeke...@verizon.net>> 
wrote:


 > Loschmidt's idea was that an isolated column of gas in a
gravitational field would develop a temperature gradient, warmer at
the top.

I believe that would be cooler at the top not warmer,. molecules at the top of a 
column of gas would have more gravitational potential energy than those at the bottom 
and so would have had to expend kinetic energy to get up that high and become cooler 
as a result. Virtually everybody agrees that this is not in violation of the second 
law but there doesn't seem to be a consensus on exactly why it doesn't.


I think the answer probably lies in the fact that the situation described is not 
stable -- the system is not in thermal equilibrium. As stated, the gas at the top of 
the column tends to be cooler because of the higher gravitational potential. But 
again, as Brent points out, the warmer gas at the bottom tends to rise, so convection 
currents act to counter the gravitational potential difference. Differences in density 
give rise to convection. If there is no heat transfer to or from the outside, the 
system never reaches a stable equilibrium.


If there were always convection currents then mechanical energy could be extracted from 
the motion instead of from the temperature gradient.


Would it be that stable? Or would you just be in a Maxwell Demon situation. Detecting 
the convection currents would destroy them, so you couldn't actually extract useful work.


Naah, convection currents are plenty macroscopic and detectable. But again I'm not clear 
on how this is supposed to violate the second law.  I guess it's that the isolated column 
supposedly gets colder as energy is extracted so its thermodynamic entropy goes down and 
the extracted mechanical energy has zero entropy, so the net entropy is decreased.  But 
that's neglecting the gravitation. Gravitating systems have negative specific heat, so 
whenever you extract mechanical energy their temperature goes up.


Brent

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Re: Quantum Mechanics Violation of the Second Law

[Bruce Kellett]

meekerdb wrote:

On 11/22/2014 8:48 PM, Bruce Kellett wrote:

John Clark wrote:
On Sat, Nov 22, 2014 , meekerdb > wrote:


 > Loschmidt's idea was that an isolated column of gas in a
gravitational field would develop a temperature gradient, warmer at
the top.

I believe that would be cooler at the top not warmer,. molecules at 
the top of a column of gas would have more gravitational potential 
energy than those at the bottom and so would have had to expend 
kinetic energy to get up that high and become cooler as a result. 
Virtually everybody agrees that this is not in violation of the 
second law but there doesn't seem to be a consensus on exactly why it 
doesn't.


I think the answer probably lies in the fact that the situation 
described is not stable -- the system is not in thermal equilibrium. 
As stated, the gas at the top of the column tends to be cooler because 
of the higher gravitational potential. But again, as Brent points out, 
the warmer gas at the bottom tends to rise, so convection currents act 
to counter the gravitational potential difference. Differences in 
density give rise to convection. If there is no heat transfer to or 
from the outside, the system never reaches a stable equilibrium.


If there were always convection currents then mechanical energy could be 
extracted from the motion instead of from the temperature gradient.


Would it be that stable? Or would you just be in a Maxwell Demon 
situation. Detecting the convection currents would destroy them, so you 
couldn't actually extract useful work.


Bruce

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Re: Quantum Mechanics Violation of the Second Law

[meekerdb]

On 11/22/2014 8:48 PM, Bruce Kellett wrote:

John Clark wrote:
On Sat, Nov 22, 2014 , meekerdb mailto:meeke...@verizon.net>> 
wrote:


 > Loschmidt's idea was that an isolated column of gas in a
gravitational field would develop a temperature gradient, warmer at
the top.

I believe that would be cooler at the top not warmer,. molecules at the top of a column 
of gas would have more gravitational potential energy than those at the bottom and so 
would have had to expend kinetic energy to get up that high and become cooler as a 
result. Virtually everybody agrees that this is not in violation of the second law but 
there doesn't seem to be a consensus on exactly why it doesn't.


I think the answer probably lies in the fact that the situation described is not stable 
-- the system is not in thermal equilibrium. As stated, the gas at the top of the column 
tends to be cooler because of the higher gravitational potential. But again, as Brent 
points out, the warmer gas at the bottom tends to rise, so convection currents act to 
counter the gravitational potential difference. Differences in density give rise to 
convection. If there is no heat transfer to or from the outside, the system never 
reaches a stable equilibrium.


If there were always convection currents then mechanical energy could be extracted from 
the motion instead of from the temperature gradient.


Brent

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Re: Quantum Mechanics Violation of the Second Law

[Bruce Kellett]

John Clark wrote:
On Sat, Nov 22, 2014 , meekerdb > wrote:


 > Loschmidt's idea was that an isolated column of gas in a
gravitational field would develop a temperature gradient, warmer at
the top. 



I believe that would be cooler at the top not warmer,. molecules at the 
top of a column of gas would have more gravitational potential energy 
than those at the bottom and so would have had to expend kinetic energy 
to get up that high and become cooler as a result. Virtually everybody 
agrees that this is not in violation of the second law but there doesn't 
seem to be a consensus on exactly why it doesn't.


I think the answer probably lies in the fact that the situation 
described is not stable -- the system is not in thermal equilibrium. As 
stated, the gas at the top of the column tends to be cooler because of 
the higher gravitational potential. But again, as Brent points out, the 
warmer gas at the bottom tends to rise, so convection currents act to 
counter the gravitational potential difference. Differences in density 
give rise to convection. If there is no heat transfer to or from the 
outside, the system never reaches a stable equilibrium.


Bruce

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Re: Quantum Mechanics Violation of the Second Law

[LizR]

Every time something appears to violate the 2nd law, gravity is involved.
There is some sort of tension between thermodynamic and gravitational
equilibrium, although obviously any system far from equilibrium should tend
towards it (if it does anything at all). (Hence my stipulation of flat
space when I try to derive the AOT from cosmic expansion.)

On 23 November 2014 at 10:09, John Clark  wrote:

> On Sat, Nov 22, 2014 , meekerdb  wrote:
>
> > Loschmidt's idea was that an isolated column of gas in a gravitational
>> field would develop a temperature gradient, warmer at the top.
>>
>
> I believe that would be cooler at the top not warmer,. molecules at the
> top of a column of gas would have more gravitational potential energy than
> those at the bottom and so would have had to expend kinetic energy to get
> up that high and become cooler as a result. Virtually everybody agrees that
> this is not in violation of the second law but there doesn't seem to be a
> consensus on exactly why it doesn't.
>
>   John K Clark
>
>
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Re: Quantum Mechanics Violation of the Second Law

[John Clark]

On Sat, Nov 22, 2014 at 6:13 PM, George  wrote:

 > I love the quote from Arthur Eddington. Let me have  the pleasure to
> cite it for you.
>
> "If your theory is found to be against the second law of thermodynamics, I
> give you no hope; there is nothing for it but to collapse in deepest
> humiliation."
>
>  This quote is an ad hominem
>

You'l have to forgive me but "ad hominem" struck a nerve; I once wrote that
a person who immediately after 911 said that Osama Bin Laden didn't want to
kill American civilians was stupid, and then a whole lot of stupid people
hit me with that pompous Latin phrase.

> threat to any researcher who dares even to think about breaking the
> Second Law.
>

The only way the Second Law could be false is if there are more ways to be
organized than disorganized, that is to say fewer ways that require lots of
information to explain how the parts of a system are arranged than ways
that require little information on how the parts of a system are arranged.
And that is why in all of physics the Second Law  is the one I'm most
certain is correct. And not only am I certain I might even be correct too.

> I know reviewers - good friends of mine - who put review papers aside the
> minute they spot any mention of the Second Law.
>

Sound like you have some smart friends who know that life is short and
realize that time spend contemplating theories the violate the Second Law
is time spent not doing something else. If a theory of physics violates the
laws of arithmetic it would be foolish to spend more time on it, I feel the
same way about theories that violate the second law.

  John K Clark

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Re: Quantum Mechanics Violation of the Second Law

[meekerdb]

On 11/22/2014 3:13 PM, George wrote:

Hi Liz, Brent, John

I love the quote from Arthur Eddington. Let me have  the pleasure to cite it 
for you.

"If your theory is found to be against the second law of thermodynamics, I 
give you
no hope; there is nothing for it but to collapse in deepest humiliation."

This quote is an ad hominem threat to any researcher who dares even to think about 
breaking the Second Law. It is based on a quasi-religious belief that the Second Law is 
unbreakable and has discouraged many bright minds from engaging in a rational discussion 
on the subject. I know reviewers - good friends of mine - who put review papers aside 
the minute they spot any mention of the Second Law.


I don't mind facing arguments as long as they are rational.

Now in partial answer to Liz's question, the best way to explain this topic is to follow 
the same path that I took.

1) Understand Loschmidt' argument
2) Rebut his argument and find a better answer.

1) Understanding Loschmidt's argument (I am quoting a passage from one of my 
papers)

"Let us begin by assuming a gas column in a gravitational field is in a 
stable
_isothermal equilibrium_ such that _no macroscopic convection current_ 
exists.
At the /microscopic/ scale, however, molecules are still moving and 
colliding
with each other. Between collisions, (i.e., along their mean free 
paths) the
molecules remain adiabatic (no heat transfer between them). Consider a 
molecule
rising against the gravitational field. It loses kinetic energy and 
therefore,
on the average, becomes colder than its environment until it collides 
and
exchanges energy with another molecule at a higher elevation. 
Similarly, a
descending molecule gains energy and, on the average, becomes hotter 
than its
environment until its next collision at a lower elevation when it can 
exchange
energy. On the average, heat is extracted from the molecule’s 
environment at the
top of a molecular path and deposited into the molecule’s environment 
at the
bottom of its path. The net effect is a downward heat transfer. Since 
heat is
actually being transferred from one elevation to another, the 
temperature
distribution ceases to be isothermal and the entropy of the gas 
increases as the
column /spontaneously/ shifts toward the adiabatic state.



You seem to use "adiabatic" in some non-standard sense.  It means with no heat or matter 
transfer into or out of the system.  You've assumed the system is isolated and hence 
whatever it does is adiabatic.  There's no such thing as an "adiabatic state" only 
adiabatic processes and the heat transfer from one part of an isolated system to another 
is an adiabatic process.



Such repeated heat transfers cause the temperature gradient to shift 
until the
drop in temperature of the gas matches the adiabatic temperature lapse 
rate. The
gas is then in an adiabatic state and the drop in temperature is the 
adiabatic
lapse rate. All vertical heat transfers then stop. /This paradoxical 
movement of
heat by diffusion from cold to hot, is accompanied by an increase in 
entropy. It
is spontaneous and can be likened to an endothermic process."
/

For a while I was absolutely convinced that Loschmidt was right. However, extensive 
Monte Carlo simulations and more analysis clearly indicated that he was wrong. Can you 
spot the flaw in the above reasoning (without having to invoke the Second Law, obviously)?


It seems to overlook a countervailing tendency, i.e. that faster moving (i.e. hot) 
molecules are more likely to be able to reach the top of the column.  And of course 
convection will tend to send warmer gas up, so Loschmidt's argument depends on there being 
no convection.


On a future post I will rebut Loschmidt's argument but show that some of it can still be 
salvaged.


What about experimental results. Hasn't someone tried to decide in the laboratory whether 
Maxwell of Loschidt was right?


Brent

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Re: Quantum Mechanics Violation of the Second Law

[George]

Hi Liz, Brent, John

I love the quote from Arthur Eddington. Let me have  the pleasure to 
cite it for you.


   "If your theory is found to be against the second law of
   thermodynamics, I give you no hope; there is nothing for it but to
   collapse in deepest humiliation."

This quote is an ad hominem threat to any researcher who dares even to 
think about breaking the Second Law. It is based on a quasi-religious 
belief that the Second Law is unbreakable and has discouraged many 
bright minds from engaging in a rational discussion on the subject. I 
know reviewers - good friends of mine - who put review papers aside the 
minute they spot any mention of the Second Law.


I don't mind facing arguments as long as they are rational.

Now in partial answer to Liz's question, the best way to explain this 
topic is to follow the same path that I took.

1) Understand Loschmidt' argument
2) Rebut his argument and find a better answer.

1) Understanding Loschmidt's argument (I am quoting a passage from one 
of my papers)


   "Let us begin by assuming a gas column in a gravitational field
   is in a stable _isothermal equilibrium_ such that _no
   macroscopic convection current_ exists. At the /microscopic/
   scale, however, molecules are still moving and colliding with
   each other. Between collisions, (i.e., along their mean free
   paths) the molecules remain adiabatic (no heat transfer between
   them). Consider a molecule rising against the gravitational
   field. It loses kinetic energy and therefore, on the average,
   becomes colder than its environment until it collides and
   exchanges energy with another molecule at a higher elevation.
   Similarly, a descending molecule gains energy and, on the
   average, becomes hotter than its environment until its next
   collision at a lower elevation when it can exchange energy. On
   the average, heat is extracted from the molecule’s environment
   at the top of a molecular path and deposited into the molecule’s
   environment at the bottom of its path. The net effect is a
   downward heat transfer. Since heat is actually being transferred
   from one elevation to another, the temperature distribution
   ceases to be isothermal and the entropy of the gas increases as
   the column /spontaneously/ shifts toward the adiabatic state.
   Such repeated heat transfers cause the temperature gradient to
   shift until the drop in temperature of the gas matches the
   adiabatic temperature lapse rate. The gas is then in an
   adiabatic state and the drop in temperature is the adiabatic
   lapse rate. All vertical heat transfers then stop. /This
   paradoxical movement of heat by diffusion from cold to hot, is
   accompanied by an increase in entropy. It is spontaneous and can
   be likened to an endothermic process."
   /

For a while I was absolutely convinced that Loschmidt was right. 
However, extensive Monte Carlo simulations and more analysis clearly 
indicated that he was wrong. Can you spot the flaw in the above 
reasoning (without having to invoke the Second Law, obviously)?


On a future post I will rebut Loschmidt's argument but show that some of 
it can still be salvaged.


Best

George

On 11/22/2014 1:09 PM, John Clark wrote:
On Sat, Nov 22, 2014 , meekerdb > wrote:


> Loschmidt's idea was that an isolated column of gas in a
gravitational field would develop a temperature gradient, warmer
at the top.


I believe that would be cooler at the top not warmer,. molecules at 
the top of a column of gas would have more gravitational potential 
energy than those at the bottom and so would have had to expend 
kinetic energy to get up that high and become cooler as a result. 
Virtually everybody agrees that this is not in violation of the second 
law but there doesn't seem to be a consensus on exactly why it doesn't.


  John K Clark


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Re: Quantum Mechanics Violation of the Second Law

[meekerdb]

On 11/22/2014 1:09 PM, John Clark wrote:

On Sat, Nov 22, 2014 , meekerdb mailto:meeke...@verizon.net>> wrote:

> Loschmidt's idea was that an isolated column of gas in a gravitational 
field would
develop a temperature gradient, warmer at the top.




You're right - just a brain slip on my part.

I believe that would be cooler at the top not warmer,. molecules at the top of a column 
of gas would have more gravitational potential energy than those at the bottom and so 
would have had to expend kinetic energy to get up that high and become cooler as a 
result. Virtually everybody agrees that this is not in violation of the second law but 
there doesn't seem to be a consensus on exactly why it doesn't.


ISTM it's just an laboratory example of what a star was once thought to do.  Before 
nuclear decay was discovered, Lord Kelvin (William Thompson), calculated the life time of 
the Sun assuming its energy came entirely from gravitational collapse.  His estimate was 
no more than a few tens of millions of years.  Darwin estimated that evolution would have 
required at least an order of magnitude longer. So Darwin seriously considered that 
Thompson had proven evolution wrong.  If he had just looked at it the other way around he 
might be credited with discovering nuclear energy as well as evolution!


The stars conversion of gravitational energy to radiation doesn't violate the 2nd law 
because the radiation photon states are much more numerous than the remaining matter states.


Brent

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Re: Quantum Mechanics Violation of the Second Law

[John Clark]

On Sat, Nov 22, 2014 , meekerdb  wrote:

> Loschmidt's idea was that an isolated column of gas in a gravitational
> field would develop a temperature gradient, warmer at the top.
>

I believe that would be cooler at the top not warmer,. molecules at the top
of a column of gas would have more gravitational potential energy than
those at the bottom and so would have had to expend kinetic energy to get
up that high and become cooler as a result. Virtually everybody agrees that
this is not in violation of the second law but there doesn't seem to be a
consensus on exactly why it doesn't.

  John K Clark

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Re: Quantum Mechanics Violation of the Second Law

[meekerdb]

On 11/21/2014 10:39 PM, LizR wrote:
Is it possible to explain to a person of modest intelligence such as myself exacty how 
you're violating the 2nd law?


(Otherwise I may feel compelled to quote Arthur Eddington...)


Loschmidt's idea was that an isolated column of gas in a gravitational field would develop 
a temperature gradient, warmer at the top.  So you could place some working fluid at the 
bottom, get it warm, then move it to top and run a heat engine off the temperature 
different getting some increment of work and dumping some heat into the upper part of the 
column.  But after some time the gradient will be reestablished and you can lower the 
working fluid and repeat the process.  Thus you will extract work from a system that is in 
equilibrium.  Of course the gas in the column will get cooler as you extract energy, so 
it's not really clear to me that the 2nd law is violated.  Gravity is different in that 
gravitating systems have negative specific heat.


Brent

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Re: Quantum Mechanics Violation of the Second Law

[LizR]

Is it possible to explain to a person of modest intelligence such as myself
exacty how you're violating the 2nd law?

(Otherwise I may feel compelled to quote Arthur Eddington...)

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Re: Quantum Mechanics Violation of the Second Law

[meekerdb]

On 11/21/2014 2:44 PM, George wrote:


If one considers an exponential distribution such as
e^(-KE-PE)
where PE is a function of elevation
then at ground level one would have
e^(-KE)
and at a given elevation h
e^(-KE-PE) = e^(-PE)e^(-KE)
Renormalizing for the lower density the distribution at elevation becomes
e^(-KE)
which is identical with the original distribution at ground level and indicates that the 
gas is isothermal. This only works with exponential distributions.


The Maxwell Boltzmann distribution can be written in several versions.
See http://homepage.univie.ac.at/franz.vesely/sp_english/sp/node8.html
The one that describes the velocity distribution is exponential:
\begin{displaymath} f(\vec{v}) = \left[ \frac{m}{2 \pi kT} \right]^{3/2} e^{-mv^{2}/2 
kT} \end{displaymath}


No, that's a Gaussian distribution over v.


but a Boltzmann term needs to be added to describe the effect of potential 
energy

\begin{displaymath} f(\vec{v}) = \left[ \frac{m}{2 \pi kT} \right]^{3/2} e^{-mv^{2}/2 
kT} \end{displaymath}  e^-(PE/kT)


This density in velocity space is commonly called*Maxwell-Boltzmann distribution 
density*. The same name is also used for a slightly different object, namely the 
distribution density of the*modulus*of the particle velocity (the ``speed'')
\begin{displaymath} f(\vert \vec{v} \vert) = 4 \pi v^{2} f(\vec{v}) = 4 \pi \left[ 
\frac{m}{2 \pi k T} \right]^{3/2} v^{2}e^{-mv^{2}/2kT} \end{displaymath}


(Similarly a Boltzmann term needs to be added. This distribution is not exponential as 
it has the v^2 factor in front. )


And also in the exponent.

Brent

My problem is to justify using the exponential distribution, obviously without having to 
invoke the Second Law which is being challenged.



On 11/21/2014 11:19 AM, meekerdb wrote:

On 11/20/2014 9:07 PM, George wrote:

Brent you are right.
Maxwell distribution is not exponential with energy. For the purpose of comparing the 
different distributions, I was attempting to give the same form to all distributions 
Maxwell, Fermi-Dirac and Bose-Einstein independently of the scaling factor in front of 
the exponential. i.e.,


The trouble is that it's not just a scaling factor in front, it's a normalization and 
the normalization has to produce the right dimensions.  The functions you right below 
are all dimensionless, so they can only be density functions relative to a 
dimensionless variable, e.g. x=(E/kT)



Maxwell: 1/e^x
Fermi-Dirac 1/(e^x  + 1)
Bose-Einstein: 1/(e^x  - 1)
I may not have been correct in doing this.

I agree, Maxwell distribution is not exponential with _energy_.

If we assume that the distribution is also not exponential with _elevation_ then the 
renormalized distribution after vertical translation does not overlap the original 
distribution. Therefore there is a spontaneous atmospheric temperature lapse and 
Loschmidt was right after all!


There is a "spontaneous" atmospheric lapse rate which in the standard atmosphere model 
is linear, -6.5degK/km, from sea level to 10km.  And you could run a heat engine using 
the temperature difference - just as people have proposed running a heat engine between 
warm surface water and cold deep ocean water.  But why would that violate the 2nd law?  
The atmosphere is heated by the surface where sunlight is absorbed and it's lost by 
radiation to space in the upper atmosphere - so there's a gradient and free energy 
which can be turned into work.
Loschmidt assumed that the temperature gradient would be self regenerating independently 
of the sun and wind.


He proposed that in an isolated column the gradient would regenerate and so you could 
repeatedly extract work from the temperature difference.  But in an isolated system this 
would reduce the energy in the system, so you couldn't get perpetual motion.


Brent





Breaking the Second Law does not require QM.  All that is required is a Maxwellian gas 
in a force field.


The question therefore is whether Maxwell distribution is exponential with 
_elevation_.


What does it mean for the M-B distribution to be exponential with elevation? 

See my comment on top of post.
As a density function over energy it has one parameter, kT.  Are you asking whether 
T=T_0*exp(-h/h_0) where T_0 is the surface temperature, h is the altitude, and h_0 is 
some altitude scale. If so, the answer is no.  The function is T=T_0 - 6.5h for T in 
degK and h in km.  But that only works up to 10km.  Changes in molecular species 
(different masses) become important at higher altitude.


If it is then Loschmidt falls on Maxwellian gases. If it is not, then Loschmidt is 
completely vindicated for any kind of gas. I need to think about this. Any idea?


Loschmidt considered just a gas or other substance in an isolated column (no solar 
heating, no radiative cooling), so the atmosphere isn't a good example.
This is the example he used. As good physicist do,we can always run a thought experiment 
in which a column of gas in a gravitational field is iso

Re: Quantum Mechanics Violation of the Second Law

[George]

If one considers an exponential distribution such as
e^(-KE-PE)
where PE is a function of elevation
then at ground level one would have
e^(-KE)
and at a given elevation h
e^(-KE-PE) = e^(-PE)e^(-KE)
Renormalizing for the lower density the distribution at elevation becomes
e^(-KE)
which is identical with the original distribution at ground level and 
indicates that the gas is isothermal. This only works with exponential 
distributions.


The Maxwell Boltzmann distribution can be written in several versions.
See http://homepage.univie.ac.at/franz.vesely/sp_english/sp/node8.html
The one that describes the velocity distribution is exponential:
\begin{displaymath} f(\vec{v}) = \left[ \frac{m}{2 \pi kT} \right]^{3/2} 
e^{-mv^{2}/2 kT} \end{displaymath}
but a Boltzmann term needs to be added to describe the effect of 
potential energy


\begin{displaymath} f(\vec{v}) = \left[ \frac{m}{2 \pi kT} \right]^{3/2} 
e^{-mv^{2}/2 kT} \end{displaymath} e^-(PE/kT)


This density in velocity space is commonly called*Maxwell-Boltzmann 
distribution density*. The same name is also used for a slightly 
different object, namely the distribution density of the*modulus*of the 
particle velocity (the ``speed'')
\begin{displaymath} f(\vert \vec{v} \vert) = 4 \pi v^{2} f(\vec{v}) = 4 
\pi \left[ \frac{m}{2 \pi k T} \right]^{3/2} v^{2}e^{-mv^{2}/2kT} 
\end{displaymath}
(Similarly a Boltzmann term needs to be added. This distribution is not 
exponential as it has the v^2 factor in front. )
My problem is to justify using the exponential distribution, obviously 
without having to invoke the Second Law which is being challenged.



On 11/21/2014 11:19 AM, meekerdb wrote:

On 11/20/2014 9:07 PM, George wrote:

Brent you are right.
Maxwell distribution is not exponential with energy. For the purpose 
of comparing the different distributions, I was attempting to give 
the same form to all distributions Maxwell, Fermi-Dirac and 
Bose-Einstein independently of the scaling factor in front of the 
exponential. i.e.,


The trouble is that it's not just a scaling factor in front, it's a 
normalization and the normalization has to produce the right 
dimensions.  The functions you right below are all dimensionless, so 
they can only be density functions relative to a dimensionless 
variable, e.g. x=(E/kT)



Maxwell: 1/e^x
Fermi-Dirac 1/(e^x  + 1)
Bose-Einstein: 1/(e^x  - 1)
I may not have been correct in doing this.

I agree, Maxwell distribution is not exponential with _energy_.

If we assume that the distribution is also not exponential with 
_elevation_ then the renormalized distribution after vertical 
translation does not overlap the original distribution. Therefore 
there is a spontaneous atmospheric temperature lapse and Loschmidt 
was right after all!


There is a "spontaneous" atmospheric lapse rate which in the standard 
atmosphere model is linear, -6.5degK/km, from sea level to 10km.  And 
you could run a heat engine using the temperature difference - just as 
people have proposed running a heat engine between warm surface water 
and cold deep ocean water.  But why would that violate the 2nd law?  
The atmosphere is heated by the surface where sunlight is absorbed and 
it's lost by radiation to space in the upper atmosphere - so there's a 
gradient and free energy which can be turned into work.
Loschmidt assumed that the temperature gradient would be self 
regenerating independently of the sun and wind.




Breaking the Second Law does not require QM.  All that is required is 
a Maxwellian gas in a force field.


The question therefore is whether Maxwell distribution is exponential 
with _elevation_.


What does it mean for the M-B distribution to be exponential with 
elevation? 

See my comment on top of post.
As a density function over energy it has one parameter, kT.  Are you 
asking whether T=T_0*exp(-h/h_0) where T_0 is the surface temperature, 
h is the altitude, and h_0 is some altitude scale. If so, the answer 
is no.  The function is T=T_0 - 6.5h for T in degK and h in km.  But 
that only works up to 10km.  Changes in molecular species (different 
masses) become important at higher altitude.


If it is then Loschmidt falls on Maxwellian gases. If it is not, then 
Loschmidt is completely vindicated for any kind of gas. I need to 
think about this. Any idea?


Loschmidt considered just a gas or other substance in an isolated 
column (no solar heating, no radiative cooling), so the atmosphere 
isn't a good example.
This is the example he used. As good physicist do,we can always run a 
thought experiment in which a column of gas in a gravitational field is 
isolated from its surrounding.


Brent



George

On 11/20/2014 6:41 PM, meekerdb wrote:

On 11/20/2014 6:28 PM, George wrote:

Maxwell's distribution

f = e^(-E/kT) where E = (1/2) mv^2


?? Distribution with respect to energy is:

Note the sqrt(E) factor. 
http://en.wikipedia.org/wiki/Maxwell-Boltzmann_distribution


Brent



can be looked at in different ways. It is a Chi S

Re: Quantum Mechanics Violation of the Second Law

[meekerdb]

On 11/20/2014 9:07 PM, George wrote:

Brent you are right.
Maxwell distribution is not exponential with energy. For the purpose of comparing the 
different distributions, I was attempting to give the same form to all distributions 
Maxwell, Fermi-Dirac and Bose-Einstein independently of the scaling factor in front of 
the exponential. i.e.,


The trouble is that it's not just a scaling factor in front, it's a normalization and the 
normalization has to produce the right dimensions.  The functions you right below are all 
dimensionless, so they can only be density functions relative to a dimensionless variable, 
e.g. x=(E/kT)



Maxwell: 1/e^x
Fermi-Dirac 1/(e^x  + 1)
Bose-Einstein: 1/(e^x  - 1)
I may not have been correct in doing this.

I agree, Maxwell distribution is not exponential with _energy_.

If we assume that the distribution is also not exponential with _elevation_ then the 
renormalized distribution after vertical translation does not overlap the original 
distribution. Therefore there is a spontaneous atmospheric temperature lapse and 
Loschmidt was right after all!


There is a "spontaneous" atmospheric lapse rate which in the standard atmosphere model is 
linear, -6.5degK/km, from sea level to 10km.  And you could run a heat engine using the 
temperature difference - just as people have proposed running a heat engine between warm 
surface water and cold deep ocean water.  But why would that violate the 2nd law?  The 
atmosphere is heated by the surface where sunlight is absorbed and it's lost by radiation 
to space in the upper atmosphere - so there's a gradient and free energy which can be 
turned into work.


Breaking the Second Law does not require QM.  All that is required is a Maxwellian gas 
in a force field.


The question therefore is whether Maxwell distribution is exponential with 
_elevation_.


What does it mean for the M-B distribution to be exponential with elevation?  As a density 
function over energy it has one parameter, kT.  Are you asking whether T=T_0*exp(-h/h_0) 
where T_0 is the surface temperature, h is the altitude, and h_0 is some altitude scale.  
If so, the answer is no.  The function is T=T_0 - 6.5h for T in degK and h in km.  But 
that only works up to 10km.  Changes in molecular species (different masses) become 
important at higher altitude.


If it is then Loschmidt falls on Maxwellian gases. If it is not, then Loschmidt is 
completely vindicated for any kind of gas. I need to think about this. Any idea?


Loschmidt considered just a gas or other substance in an isolated column (no solar 
heating, no radiative cooling), so the atmosphere isn't a good example.


Brent



George

On 11/20/2014 6:41 PM, meekerdb wrote:

On 11/20/2014 6:28 PM, George wrote:

Maxwell's distribution

f = e^(-E/kT) where E = (1/2) mv^2


?? Distribution with respect to energy is:

Note the sqrt(E) factor. 
http://en.wikipedia.org/wiki/Maxwell-Boltzmann_distribution

Brent



can be looked at in different ways. It is a Chi Square distribution with respect to 
velocity v, and exponential with respect to kinetic energy E.

The _most likely (mode)_ kinetic energy is zero


Not for a Maxwell-Boltzmann distribution.


Brent

but the _mean_ kinetic energy is not zero . The distribution decays exponentially with 
higher energies.

George

On 11/20/2014 6:13 PM, meekerdb wrote:
If it were the momentum or velocity the mean would be zero, but it wouldn't be 
exponential.  If you just considered the speed (absolute magnitude of velocity) in a 
particular direction you get an exponential distribution.  Is that what the graph 
represents?


Brent

On 11/20/2014 5:03 PM, LizR wrote:
The average kinetic energy of an air molecule is zero, I imagine, because they're 
all travelling in different directions and cancel out? Or doesn't it work like that?






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Re: Quantum Mechanics Violation of the Second Law

[Bruno Marchal]

On 21 Nov 2014, at 00:57, George wrote:


Thanks Bruno, Liz and Richard for your responses.

The topic is extremely controversial…


OK.



It took me a few months of sleepless nights to come to term with  
these ideas…. but let reason prevail. I am looking forward to an  
open and rational discussion… a background in statistical  
thermodynamics would be helpful.


I will have to revise that. It is a subtle domain. I have been wrong  
on Maxwell daemon more than once, and I have still not a good  
intuition of Landauer and Zurek works on this.






Bruno, you may not be able to download my pdf file because your  
Adobe Reader is not up to date.


Yeah, my poor old computer can't update anything, and I should as soon  
as possible buy a new one.





If you wish I could simply attach these files to my email. Please  
let me know.


With pleasure. keep in mind that I am not a physicist. Just a modest  
mathematical theologian :)




You asked me to summarize my post. The best way is with pictures  
taken from my paper#2.https://sites.google.com/a/entropicpower.com/entropicpower-com/Thermoelectric_Adiabatic_Effects_Due_to_Non-Maxwellian_Carrier_Distribution.pdf?attredirects=0&d=1 
   (Currently under review)


Figure 7 shows what happens to the energy distribution of a  
Maxwellian gas (e.g. air) as molecules rise from ground level (red)  
to a given altitude (blue). Kinetic energy is converted to potential  
energy and the distribution shifts to the left.


However when the distribution is renormalized as shown in Figure 8,  
the original distribution is recovered, implying that the gas is  
isothermal with elevation. The Second Law is upheld and Loschmidt is  
proven wrong….. but only with respect to Maxwellian gases.


Now see what happens when a Fermi-Dirac gas (carriers in a  
semiconductor) is subjected to a force field as shown in Figure 9.  
The distribution is shifted to the left as elevation increases.  
However, renormalization does not recover the original distribution  
because it is not exponential. The lower elevation has a higher  
temperature than the higher elevation. The Second Law is broken.  
This effect can only be observed in high quality thermoelectric  
materials (Caltech experiment).


I have made this calculator program and a simulator publicly  
available at my web site.


Figure. 7. Un-normalized Maxwell distribution at ground (red/thick)  
and at non-zero elevation (blue/thin) showing a shift to a lower  
kinetic energy, a drop in density and a drop in temperature.


Figure. 8. Renormalized shifted Maxwell distribution at non-zero  
elevation (blue/thin) is identical to original non-shifted  
distribution at ground level (red/thick).



Figure. 11. Un-normalized Fermi-Dirac distribution at ground (red/ 
thick) and non-zero elevation (blue/thin) showing drop in density  
and drop in temperature.



Figure. 12. Renormalized Fermi-Dirac distributions at ground level  
(red/thick) and at elevation (blue/thin) are different. Elevation  
lowers energy and temperature of gas.




Please look on the right of the pictures for the temperatures at the  
ceiling and at the floor.



I will look at this, revise a bit of thermodynamic, and let you know  
if I understand the point. It seems amazing.


Best,

Bruno






George Levy



On 11/20/2014 1:16 PM, LizR wrote:
This is very interesting, if I can just get my head round it.  
"Traditional" thermodynamics basically tells us that a closed  
system in a macroscopically distinct state (and that is able to do  
so) will evolve with high probability towards a state that is  
macroscopically indistinguishable from most of the other states it  
can evolve into. However using quantum phenomena like entanglement  
and uncertainty could root this apparently emergent statistical  
phenomenon in some fundamental physics. Since the "emergent"  
version should work anyway - with virtually any laws of physics -  
we appear to have a surfeit of explanatory power!


However I need to get my head around it some more.

On 21 November 2014 07:26, Richard Ruquist  wrote:
"statistical-mechanical ensembles arise naturally from quantum  
entanglement"


http://people.physics.anu.edu.au/~tas110/Teaching/Lectures/L5/Material/Lloyd06.pdf

a lecture given by Seth Lloyd

QUANTUM THERMODYNAMICS
Excuse our ignorance
Classically, the second law of thermodynamics implies that our  
knowledge about
a system always decreases. A more flattering interpretation  
connects entropy

with entanglement inherent to quantum mechanics.
SETH LLOYD
is in the Department of Mechanical Engineering,
Massachusetts Institute of Technology, 77 Massachusetts
Avenue, Cambridge, Massachusetts 02139-4307, USA

On Thu, Nov 20, 2014 at 11:30 AM, Bruno Marchal   
wrote:


On 20 Nov 2014, at 02:15, George wrote:


Hi everyone

This post is relevant to a few threads in this list
“Reversing time = local reversal of thermodynamic arrows?”  and  
“Two apparently different forms of entropy”.


I am so

Re: Quantum Mechanics Violation of the Second Law

[George]

Brent you are right.
Maxwell distribution is not exponential with energy. For the purpose of 
comparing the different distributions, I was attempting to give the same 
form to all distributions Maxwell, Fermi-Dirac and Bose-Einstein 
independently of the scaling factor in front of the exponential. i.e.,

Maxwell: 1/e^x
Fermi-Dirac 1/(e^x  + 1)
Bose-Einstein: 1/(e^x  - 1)
I may not have been correct in doing this.

I agree, Maxwell distribution is not exponential with _energy_.

If we assume that the distribution is also not exponential with 
_elevation_ then the renormalized distribution after vertical 
translation does not overlap the original distribution. Therefore there 
is a spontaneous atmospheric temperature lapse and Loschmidt was right 
after all! Breaking the Second Law does not require QM.  All that is 
required is a Maxwellian gas in a force field.


The question therefore is whether Maxwell distribution is exponential 
with _elevation_. If it is then Loschmidt falls on Maxwellian gases. If 
it is not, then Loschmidt is completely vindicated for any kind of gas. 
I need to think about this. Any idea?


George

On 11/20/2014 6:41 PM, meekerdb wrote:

On 11/20/2014 6:28 PM, George wrote:

Maxwell's distribution

f = e^(-E/kT) where E = (1/2) mv^2


?? Distribution with respect to energy is:

Note the sqrt(E) factor. 
http://en.wikipedia.org/wiki/Maxwell-Boltzmann_distribution


Brent



can be looked at in different ways. It is a Chi Square distribution 
with respect to velocity v, and exponential with respect to kinetic 
energy E.

The _most likely (mode)_ kinetic energy is zero


Not for a Maxwell-Boltzmann distribution.


Brent

but the _mean_ kinetic energy is not zero . The distribution decays 
exponentially with higher energies.

George

On 11/20/2014 6:13 PM, meekerdb wrote:
If it were the momentum or velocity the mean would be zero, but it 
wouldn't be exponential.  If you just considered the speed (absolute 
magnitude of velocity) in a particular direction you get an 
exponential distribution.  Is that what the graph represents?


Brent

On 11/20/2014 5:03 PM, LizR wrote:
The average kinetic energy of an air molecule is zero, I imagine, 
because they're all travelling in different directions and cancel 
out? Or doesn't it work like that?






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Re: Quantum Mechanics Violation of the Second Law

[meekerdb]

On 11/20/2014 6:28 PM, George wrote:

Maxwell's distribution

f = e^(-E/kT) where E = (1/2) mv^2


?? Distribution with respect to energy is:

f_E\,dE=f_p\left(\frac{dp}{dE}\right)\,dE =2\sqrt{\frac{E}{\pi}} \left(\frac{1}{kT} 
\right)^{3/2}\exp\left[\frac{-E}{kT}\right]\,dE.









Note the sqrt(E) factor. 
http://en.wikipedia.org/wiki/Maxwell-Boltzmann_distribution

Brent



can be looked at in different ways. It is a Chi Square distribution with respect to 
velocity v, and exponential with respect to kinetic energy E.

The _most likely (mode)_ kinetic energy is zero


Not for a Maxwell-Boltzmann distribution.


Brent

but the _mean_ kinetic energy is not zero . The distribution decays exponentially with 
higher energies.

George

On 11/20/2014 6:13 PM, meekerdb wrote:
If it were the momentum or velocity the mean would be zero, but it wouldn't be 
exponential.  If you just considered the speed (absolute magnitude of velocity) in a 
particular direction you get an exponential distribution.  Is that what the graph 
represents?


Brent

On 11/20/2014 5:03 PM, LizR wrote:
The average kinetic energy of an air molecule is zero, I imagine, because they're all 
travelling in different directions and cancel out? Or doesn't it work like that?




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Re: Quantum Mechanics Violation of the Second Law

[George]

Maxwell's distribution

f = e^(-E/kT) where E = (1/2) mv^2

can be looked at in different ways. It is a Chi Square distribution with 
respect to velocity v, and exponential with respect to kinetic energy E.
The _most likely (mode)_ kinetic energy is zero but the _mean_ kinetic 
energy is not zero . The distribution decays exponentially with higher 
energies.

George

On 11/20/2014 6:13 PM, meekerdb wrote:
If it were the momentum or velocity the mean would be zero, but it 
wouldn't be exponential.  If you just considered the speed (absolute 
magnitude of velocity) in a particular direction you get an 
exponential distribution.  Is that what the graph represents?


Brent

On 11/20/2014 5:03 PM, LizR wrote:
The average kinetic energy of an air molecule is zero, I imagine, 
because they're all travelling in different directions and cancel 
out? Or doesn't it work like that?




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Re: Quantum Mechanics Violation of the Second Law

[meekerdb]

If it were the momentum or velocity the mean would be zero, but it wouldn't be 
exponential.  If you just considered the speed (absolute magnitude of velocity) in a 
particular direction you get an exponential distribution.  Is that what the graph represents?


Brent

On 11/20/2014 5:03 PM, LizR wrote:
The average kinetic energy of an air molecule is zero, I imagine, because they're all 
travelling in different directions and cancel out? Or doesn't it work like that?


On 21 November 2014 13:09, meekerdb mailto:meeke...@verizon.net>> 
wrote:


On 11/20/2014 3:57 PM, George wrote:


Thanks Bruno, Liz and Richard for your responses.

The topic is extremely controversial… It took me a few months of sleepless 
nights
to come to term with these ideas…. but let reason prevail. I am looking 
forward to
an open and rational discussion… a background in statistical thermodynamics 
would
be helpful.

Bruno, you may not be able to download my pdf file because your Adobe 
Reader is not
up to date. If you wish I could simply attach these files to my email. 
Please let
me know. You asked me to summarize my post. The best way is with pictures 
taken
from my

paper#2.https://sites.google.com/a/entropicpower.com/entropicpower-com/Thermoelectric_Adiabatic_Effects_Due_to_Non-Maxwellian_Carrier_Distribution.pdf?attredirects=0&d=1
(Currently under review)

Figure 7 shows what happens to the energy distribution of a Maxwellian gas 
(e.g.
air) as molecules rise from ground level (red) to a given altitude (blue). 
Kinetic
energy is converted to potential energy and the distribution shifts to the 
left.



Am I correctly interpreting this curve as showing that the kinetic energy
probability density function is an exponential; so that the most probable 
kinetic
energy for an air molecule is zero??  Why isn't it the Maxwell-Boltzmann 
distribution?

Brent



However when the distribution is renormalized as shown in Figure 8, the 
original
distribution is recovered, implying that the gas is isothermal with 
elevation. The
Second Law is upheld and Loschmidt is proven wrong….. but only with respect 
to
Maxwellian gases.

Now see what happens when a Fermi-Dirac gas (carriers in a semiconductor) is
subjected to a force field as shown in Figure 9. The distribution is 
shifted to the
left as elevation increases. However, renormalization does not recover the 
original
distribution because it is not exponential. The lower elevation has a higher
temperature than the higher elevation. The Second Law is broken. This 
effect can
only be observed in high quality thermoelectric materials (Caltech 
experiment).

I have made this calculator program and a simulator publicly available at 
my web site.

*Figure. 7.* Un-normalized Maxwell distribution at ground (red/thick) and at
non-zero elevation (blue/thin) showing a shift to a lower kinetic energy, a 
drop in
density and a drop in temperature.

*Figure. 8.* Renormalized shifted Maxwell distribution at non-zero elevation
(blue/thin) is identical to original non-shifted distribution at ground 
level
(red/thick).

**

*Figure. 11.* Un-normalized Fermi-Dirac distribution at ground (red/thick) 
and
non-zero elevation (blue/thin) showing drop in density and drop in 
temperature.

*Figure. 12.* Renormalized Fermi-Dirac distributions at ground level 
(red/thick)
and at elevation (blue/thin) are different. Elevation lowers energy and 
temperature
of gas.

Please look on the right of the pictures for the temperatures at the 
ceiling and at
the floor.

George Levy




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Re: Quantum Mechanics Violation of the Second Law

[LizR]

The average kinetic energy of an air molecule is zero, I imagine, because
they're all travelling in different directions and cancel out? Or doesn't
it work like that?

On 21 November 2014 13:09, meekerdb  wrote:

>  On 11/20/2014 3:57 PM, George wrote:
>
>  Thanks Bruno, Liz and Richard for your responses.
>
>  The topic is extremely controversial… It took me a few months of
> sleepless nights to come to term with these ideas…. but let reason prevail.
> I am looking forward to an open and rational discussion… a background in
> statistical thermodynamics would be helpful.
>
>  Bruno, you may not be able to download my pdf file because your Adobe
> Reader is not up to date. If you wish I could simply attach these files to
> my email. Please let me know. You asked me to summarize my post. The best
> way is with pictures taken from my paper#2.
> https://sites.google.com/a/entropicpower.com/entropicpower-com/Thermoelectric_Adiabatic_Effects_Due_to_Non-Maxwellian_Carrier_Distribution.pdf?attredirects=0&d=1
> (Currently under review)
>
>  Figure 7 shows what happens to the energy distribution of a Maxwellian
> gas (e.g. air) as molecules rise from ground level (red) to a given
> altitude (blue). Kinetic energy is converted to potential energy and the
> distribution shifts to the left.
>
>
> Am I correctly interpreting this curve as showing that the kinetic energy
> probability density function is an exponential; so that the most probable
> kinetic energy for an air molecule is zero??  Why isn't it the
> Maxwell-Boltzmann distribution?
>
> Brent
>
>
>  However when the distribution is renormalized as shown in Figure 8, the
> original distribution is recovered, implying that the gas is isothermal
> with elevation. The Second Law is upheld and Loschmidt is proven wrong…..
> but only with respect to Maxwellian gases.
>
>  Now see what happens when a Fermi-Dirac gas (carriers in a
> semiconductor) is subjected to a force field as shown in Figure 9. The
> distribution is shifted to the left as elevation increases. However,
> renormalization does not recover the original distribution because it is
> not exponential. The lower elevation has a higher temperature than the
> higher elevation. The Second Law is broken. This effect can only be
> observed in high quality thermoelectric materials (Caltech experiment).
>
>  I have made this calculator program and a simulator publicly available
> at my web site.
>
>  *Figure. 7.* Un-normalized Maxwell distribution at ground (red/thick)
> and at non-zero elevation (blue/thin) showing a shift to a lower kinetic
> energy, a drop in density and a drop in temperature.
>
> *Figure. 8.* Renormalized shifted Maxwell distribution at non-zero
> elevation (blue/thin) is identical to original non-shifted distribution at
> ground level (red/thick).
>
>  *Figure. 11.* Un-normalized Fermi-Dirac distribution at ground
> (red/thick) and non-zero elevation (blue/thin) showing drop in density and
> drop in temperature.
>
> *Figure. 12.* Renormalized Fermi-Dirac distributions at ground level
> (red/thick) and at elevation (blue/thin) are different. Elevation lowers
> energy and temperature of gas.
>
>
>
> Please look on the right of the pictures for the temperatures at the
> ceiling and at the floor.
>
> George Levy
>
>
>
>
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Re: Quantum Mechanics Violation of the Second Law

[meekerdb]

On 11/20/2014 3:57 PM, George wrote:


Thanks Bruno, Liz and Richard for your responses.

The topic is extremely controversial… It took me a few months of sleepless nights to 
come to term with these ideas…. but let reason prevail. I am looking forward to an open 
and rational discussion… a background in statistical thermodynamics would be helpful.


Bruno, you may not be able to download my pdf file because your Adobe Reader is not up 
to date. If you wish I could simply attach these files to my email. Please let me know. 
You asked me to summarize my post. The best way is with pictures taken from my 
paper#2.https://sites.google.com/a/entropicpower.com/entropicpower-com/Thermoelectric_Adiabatic_Effects_Due_to_Non-Maxwellian_Carrier_Distribution.pdf?attredirects=0&d=1 
(Currently under review)


Figure 7 shows what happens to the energy distribution of a Maxwellian gas (e.g. air) as 
molecules rise from ground level (red) to a given altitude (blue). Kinetic energy is 
converted to potential energy and the distribution shifts to the left.




Am I correctly interpreting this curve as showing that the kinetic energy probability 
density function is an exponential; so that the most probable kinetic energy for an air 
molecule is zero??  Why isn't it the Maxwell-Boltzmann distribution?


Brent



However when the distribution is renormalized as shown in Figure 8, the original 
distribution is recovered, implying that the gas is isothermal with elevation. The 
Second Law is upheld and Loschmidt is proven wrong….. but only with respect to 
Maxwellian gases.


Now see what happens when a Fermi-Dirac gas (carriers in a semiconductor) is subjected 
to a force field as shown in Figure 9. The distribution is shifted to the left as 
elevation increases. However, renormalization does not recover the original distribution 
because it is not exponential. The lower elevation has a higher temperature than the 
higher elevation. The Second Law is broken. This effect can only be observed in high 
quality thermoelectric materials (Caltech experiment).


I have made this calculator program and a simulator publicly available at my 
web site.

*Figure. 7.* Un-normalized Maxwell distribution at ground (red/thick) and at non-zero 
elevation (blue/thin) showing a shift to a lower kinetic energy, a drop in density and a 
drop in temperature.


*Figure. 8.* Renormalized shifted Maxwell distribution at non-zero elevation (blue/thin) 
is identical to original non-shifted distribution at ground level (red/thick).


**

*Figure. 11.* Un-normalized Fermi-Dirac distribution at ground (red/thick) and non-zero 
elevation (blue/thin) showing drop in density and drop in temperature.


*Figure. 12.* Renormalized Fermi-Dirac distributions at ground level (red/thick) and at 
elevation (blue/thin) are different. Elevation lowers energy and temperature of gas.


Please look on the right of the pictures for the temperatures at the ceiling and at the 
floor.


George Levy




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Re: Quantum Mechanics Violation of the Second Law

[George]

Thanks Bruno, Liz and Richard for your responses.

The topic is extremely controversial… It took me a few months of 
sleepless nights to come to term with these ideas…. but let reason 
prevail. I am looking forward to an open and rational discussion… a 
background in statistical thermodynamics would be helpful.


Bruno, you may not be able to download my pdf file because your Adobe 
Reader is not up to date. If you wish I could simply attach these files 
to my email. Please let me know. You asked me to summarize my post. The 
best way is with pictures taken from my 
paper#2.https://sites.google.com/a/entropicpower.com/entropicpower-com/Thermoelectric_Adiabatic_Effects_Due_to_Non-Maxwellian_Carrier_Distribution.pdf?attredirects=0&d=1 
(Currently under review)


Figure 7 shows what happens to the energy distribution of a Maxwellian 
gas (e.g. air) as molecules rise from ground level (red) to a given 
altitude (blue). Kinetic energy is converted to potential energy and the 
distribution shifts to the left.


However when the distribution is renormalized as shown in Figure 8, the 
original distribution is recovered, implying that the gas is isothermal 
with elevation. The Second Law is upheld and Loschmidt is proven 
wrong….. but only with respect to Maxwellian gases.


Now see what happens when a Fermi-Dirac gas (carriers in a 
semiconductor) is subjected to a force field as shown in Figure 9. The 
distribution is shifted to the left as elevation increases. However, 
renormalization does not recover the original distribution because it is 
not exponential. The lower elevation has a higher temperature than the 
higher elevation. The Second Law is broken. This effect can only be 
observed in high quality thermoelectric materials (Caltech experiment).


I have made this calculator program and a simulator publicly available 
at my web site.


*Figure. 7.* Un-normalized Maxwell distribution at ground (red/thick) 
and at non-zero elevation (blue/thin) showing a shift to a lower kinetic 
energy, a drop in density and a drop in temperature.


*Figure. 8.* Renormalized shifted Maxwell distribution at non-zero 
elevation (blue/thin) is identical to original non-shifted distribution 
at ground level (red/thick).


**

*Figure. 11.* Un-normalized Fermi-Dirac distribution at ground 
(red/thick) and non-zero elevation (blue/thin) showing drop in density 
and drop in temperature.


*Figure. 12.* Renormalized Fermi-Dirac distributions at ground level 
(red/thick) and at elevation (blue/thin) are different. Elevation lowers 
energy and temperature of gas.


Please look on the right of the pictures for the temperatures at the 
ceiling and at the floor.


George Levy



On 11/20/2014 1:16 PM, LizR wrote:
This is very interesting, if I can just get my head round it. 
"Traditional" thermodynamics basically tells us that a closed system 
in a macroscopically distinct state (and that is able to do so) 
will evolve with high probability towards a state that is 
macroscopically indistinguishable from most of the other states it can 
evolve into. However using quantum phenomena like entanglement and 
uncertainty could root this apparently emergent statistical phenomenon 
in some fundamental physics. Since the "emergent" version should work 
anyway - with virtually /any /laws of physics - we appear to have a 
surfeit of explanatory power!


However I need to get my head around it some more.

On 21 November 2014 07:26, Richard Ruquist > wrote:


"statistical-mechanical ensembles arise naturally from quantum
entanglement"


http://people.physics.anu.edu.au/~tas110/Teaching/Lectures/L5/Material/Lloyd06.pdf



a lecture given by Seth Lloyd

QUANTUM THERMODYNAMICS
Excuse our ignorance
Classically, the second law of thermodynamics implies that our
knowledge about
a system always decreases. A more flattering interpretation
connects entropy
with entanglement inherent to quantum mechanics.
SETH LLOYD
is in the Department of Mechanical Engineering,
Massachusetts Institute of Technology, 77 Massachusetts
Avenue, Cambridge, Massachusetts 02139-4307, USA

On Thu, Nov 20, 2014 at 11:30 AM, Bruno Marchal mailto:marc...@ulb.ac.be>> wrote:


On 20 Nov 2014, at 02:15, George wrote:


Hi everyone


This post is relevant to a few threads in this list

“Reversing time = local reversal of thermodynamic arrows?”
and “Two apparently different forms of entropy”.


I am sorry that I haven’t posted to this list for a while. I
have been very busy with my work.

In my latest research I have found that Quantum Mechanics, in
particular the Pauli Exclusion Principle, can be used to go
around limitations of classical physics and break the Second Law.

Papers describing the research are publicly available

Re: Quantum Mechanics Violation of the Second Law

[LizR]

This is very interesting, if I can just get my head round it. "Traditional"
thermodynamics basically tells us that a closed system in a macroscopically
distinct state (and that is able to do so) will evolve with high
probability towards a state that is macroscopically indistinguishable from
most of the other states it can evolve into. However using quantum
phenomena like entanglement and uncertainty could root this apparently
emergent statistical phenomenon in some fundamental physics. Since the
"emergent" version should work anyway - with virtually *any *laws of
physics - we appear to have a surfeit of explanatory power!

However I need to get my head around it some more.

On 21 November 2014 07:26, Richard Ruquist  wrote:

> "statistical-mechanical ensembles arise naturally from quantum
> entanglement"
>
>
> http://people.physics.anu.edu.au/~tas110/Teaching/Lectures/L5/Material/Lloyd06.pdf
>
> a lecture given by Seth Lloyd
>
> QUANTUM THERMODYNAMICS
> Excuse our ignorance
> Classically, the second law of thermodynamics implies that our knowledge
> about
> a system always decreases. A more flattering interpretation connects
> entropy
> with entanglement inherent to quantum mechanics.
> SETH LLOYD
> is in the Department of Mechanical Engineering,
> Massachusetts Institute of Technology, 77 Massachusetts
> Avenue, Cambridge, Massachusetts 02139-4307, USA
>
> On Thu, Nov 20, 2014 at 11:30 AM, Bruno Marchal  wrote:
>
>>
>> On 20 Nov 2014, at 02:15, George wrote:
>>
>>  Hi everyone
>>
>>
>> This post is relevant to a few threads in this list
>>
>> “Reversing time = local reversal of thermodynamic arrows?”  and “Two
>> apparently different forms of entropy”.
>>
>>
>> I am sorry that I haven’t posted to this list for a while. I have been
>> very busy with my work.
>>
>> In my latest research I have found that Quantum Mechanics, in particular
>> the Pauli Exclusion Principle, can be used to go around limitations of
>> classical physics and break the Second Law.
>>
>>
>>
>> Papers describing the research are publicly available at
>>
>>
>>
>> http://www.mdpi.com/1099-4300/15/11/4700
>>
>>
>>
>> and
>>
>>
>>
>>
>> https://sites.google.com/a/entropicpower.com/entropicpower-com/Thermoelectric_Adiabatic_Effects_Due_to_Non-Maxwellian_Carrier_Distribution.pdf?attredirects=0&d=1
>> (Currently under review)
>>
>>
>>
>> Nice to hear from you George. It has been a long time indeed. I will take
>> a look, but up to now, my computer refuses to open the document ...
>>
>> To be frank, I doubt very much that QM could break the Second Law. If you
>> could sum up the reason here, it would be nice. Take your time (I am also
>> rather busy those days).
>>
>>
>> Best,
>>
>> Bruno
>>
>>
>>
>>
>> These papers describe experimentally observed thermoelectric adiabatic
>> effects (the existence of a voltage without any heat flow, and the
>> existence of a temperature differential without any input current.)
>>
>>
>>
>> Here is some background: The story begins with a thermodynamicist of the
>> nineteenth century, Josef Loschmidt, who challenged Boltzmann and Maxwell
>> regarding the Second Law. Loschmidt argued that the temperature lapse in
>> the atmosphere could be used to run a heat engine, thereby violating the
>> Second Law. Loschmidt was wrong as shall be explained below but it is
>> instructive to go through his reasoning. Loschmidt argued that the
>> atmospheric temperature lapse occurs spontaneously, is self renewing and is
>> due to the decrease in kinetic energy of molecules as they go up against
>> the gravitational gradient between collisions. Therefore the atmospheric
>> temperature decreases adiabatically with altitude and could be used to run
>> a heat engine.
>>
>> However, Loschmidt ignored the fact that molecular energies are
>> distributed over a range of values and that gravity separates the molecules
>> according to their energy in a fashion analogous to a mass spectrometer
>> separating particles according to mass. Molecules with greater energy can
>> reach greater heights. If one assigns a Maxwellian distribution to the
>> molecules (exponentially decaying function of energy), then any vertical
>> translation of a group of molecules results in a lowering of their kinetic
>> energy, corresponding to a left shift of their distribution. After the
>> distribution is renormalized to account for the lower density at higher
>> elevation, the original distribution is recovered indicating that the gas
>> is isothermal, not adiabatic as Loschmidt conjectured. This effect is due
>> to the exponential nature of the distribution. An addition (of potential
>> energy) in the exponent corresponds to a multiplication of the amplitude.
>> So Loschmidt was wrong: the Loschmidt effect (lowering of KE with
>> altitude) is exactly canceled by the energy separation effect caused by
>> gravity. However he was only wrong with respect to gases that follow
>> Maxwell’s distribution.
>>
>>
>>
>> Electrical carriers in semiconductor materials 

Re: Quantum Mechanics Violation of the Second Law

[Richard Ruquist]

"statistical-mechanical ensembles arise naturally from quantum
entanglement"

http://people.physics.anu.edu.au/~tas110/Teaching/Lectures/L5/Material/Lloyd06.pdf

a lecture given by Seth Lloyd

QUANTUM THERMODYNAMICS
Excuse our ignorance
Classically, the second law of thermodynamics implies that our knowledge
about
a system always decreases. A more flattering interpretation connects
entropy
with entanglement inherent to quantum mechanics.
SETH LLOYD
is in the Department of Mechanical Engineering,
Massachusetts Institute of Technology, 77 Massachusetts
Avenue, Cambridge, Massachusetts 02139-4307, USA

On Thu, Nov 20, 2014 at 11:30 AM, Bruno Marchal  wrote:

>
> On 20 Nov 2014, at 02:15, George wrote:
>
>  Hi everyone
>
>
> This post is relevant to a few threads in this list
>
> “Reversing time = local reversal of thermodynamic arrows?”  and “Two
> apparently different forms of entropy”.
>
>
> I am sorry that I haven’t posted to this list for a while. I have been
> very busy with my work.
>
> In my latest research I have found that Quantum Mechanics, in particular
> the Pauli Exclusion Principle, can be used to go around limitations of
> classical physics and break the Second Law.
>
>
>
> Papers describing the research are publicly available at
>
>
>
> http://www.mdpi.com/1099-4300/15/11/4700
>
>
>
> and
>
>
>
>
> https://sites.google.com/a/entropicpower.com/entropicpower-com/Thermoelectric_Adiabatic_Effects_Due_to_Non-Maxwellian_Carrier_Distribution.pdf?attredirects=0&d=1
> (Currently under review)
>
>
>
> Nice to hear from you George. It has been a long time indeed. I will take
> a look, but up to now, my computer refuses to open the document ...
>
> To be frank, I doubt very much that QM could break the Second Law. If you
> could sum up the reason here, it would be nice. Take your time (I am also
> rather busy those days).
>
>
> Best,
>
> Bruno
>
>
>
>
> These papers describe experimentally observed thermoelectric adiabatic
> effects (the existence of a voltage without any heat flow, and the
> existence of a temperature differential without any input current.)
>
>
>
> Here is some background: The story begins with a thermodynamicist of the
> nineteenth century, Josef Loschmidt, who challenged Boltzmann and Maxwell
> regarding the Second Law. Loschmidt argued that the temperature lapse in
> the atmosphere could be used to run a heat engine, thereby violating the
> Second Law. Loschmidt was wrong as shall be explained below but it is
> instructive to go through his reasoning. Loschmidt argued that the
> atmospheric temperature lapse occurs spontaneously, is self renewing and is
> due to the decrease in kinetic energy of molecules as they go up against
> the gravitational gradient between collisions. Therefore the atmospheric
> temperature decreases adiabatically with altitude and could be used to run
> a heat engine.
>
> However, Loschmidt ignored the fact that molecular energies are
> distributed over a range of values and that gravity separates the molecules
> according to their energy in a fashion analogous to a mass spectrometer
> separating particles according to mass. Molecules with greater energy can
> reach greater heights. If one assigns a Maxwellian distribution to the
> molecules (exponentially decaying function of energy), then any vertical
> translation of a group of molecules results in a lowering of their kinetic
> energy, corresponding to a left shift of their distribution. After the
> distribution is renormalized to account for the lower density at higher
> elevation, the original distribution is recovered indicating that the gas
> is isothermal, not adiabatic as Loschmidt conjectured. This effect is due
> to the exponential nature of the distribution. An addition (of potential
> energy) in the exponent corresponds to a multiplication of the amplitude.
> So Loschmidt was wrong: the Loschmidt effect (lowering of KE with
> altitude) is exactly canceled by the energy separation effect caused by
> gravity. However he was only wrong with respect to gases that follow
> Maxwell’s distribution.
>
>
>
> Electrical carriers in semiconductor materials are Fermions following
> Fermi-Dirac statistics and the above argument does not apply to them. When
> subjected to a voltage they do develop a temperature gradient. This
> temperature differential is hard to observe because it is promptly shorted
> by heat phonons. As experiments at Caltech have shown (see my papers), it
> can be observed in certain circumstances such as in high Z thermoelectric
> materials in which electrical carriers and heat phonons are strongly
> decoupled. The Onsager reciprocal of the temperature differential is a
> voltage differential which has also been experimentally observed.
>
>
>
> The two papers above describe these results in detail.
>
>
>
> In summary, quantum mechanics, in particular the Pauli Exclusion
> Principle, can be used to bypass classical mechanics in generating
> macroscopic effects violating the Second Law.
>
>

Re: Quantum Mechanics Violation of the Second Law

[Bruno Marchal]

On 20 Nov 2014, at 02:15, George wrote:


Hi everyone

This post is relevant to a few threads in this list
“Reversing time = local reversal of thermodynamic arrows?”  and “Two  
apparently different forms of entropy”.


I am sorry that I haven’t posted to this list for a while. I have  
been very busy with my work.
In my latest research I have found that Quantum Mechanics, in  
particular the Pauli Exclusion Principle, can be used to go around  
limitations of classical physics and break the Second Law.


Papers describing the research are publicly available at

http://www.mdpi.com/1099-4300/15/11/4700

and

https://sites.google.com/a/entropicpower.com/entropicpower-com/Thermoelectric_Adiabatic_Effects_Due_to_Non-Maxwellian_Carrier_Distribution.pdf?attredirects=0&d=1 
   (Currently under review)



Nice to hear from you George. It has been a long time indeed. I will  
take a look, but up to now, my computer refuses to open the document ...


To be frank, I doubt very much that QM could break the Second Law. If  
you could sum up the reason here, it would be nice. Take your time (I  
am also rather busy those days).



Best,

Bruno





These papers describe experimentally observed thermoelectric  
adiabatic effects (the existence of a voltage without any heat flow,  
and the existence of a temperature differential without any input  
current.)


Here is some background: The story begins with a thermodynamicist of  
the nineteenth century, Josef Loschmidt, who challenged Boltzmann  
and Maxwell regarding the Second Law. Loschmidt argued that the  
temperature lapse in the atmosphere could be used to run a heat  
engine, thereby violating the Second Law. Loschmidt was wrong as  
shall be explained below but it is instructive to go through his  
reasoning. Loschmidt argued that the atmospheric temperature lapse  
occurs spontaneously, is self renewing and is due to the decrease in  
kinetic energy of molecules as they go up against the gravitational  
gradient between collisions. Therefore the atmospheric temperature  
decreases adiabatically with altitude and could be used to run a  
heat engine.


However, Loschmidt ignored the fact that molecular energies are  
distributed over a range of values and that gravity separates the  
molecules according to their energy in a fashion analogous to a mass  
spectrometer separating particles according to mass. Molecules with  
greater energy can reach greater heights. If one assigns a  
Maxwellian distribution to the molecules (exponentially decaying  
function of energy), then any vertical translation of a group of  
molecules results in a lowering of their kinetic energy,  
corresponding to a left shift of their distribution. After the  
distribution is renormalized to account for the lower density at  
higher elevation, the original distribution is recovered indicating  
that the gas is isothermal, not adiabatic as Loschmidt conjectured.  
This effect is due to the exponential nature of the distribution. An  
addition (of potential energy) in the exponent corresponds to a  
multiplication of the amplitude.  So Loschmidt was wrong: the  
Loschmidt effect (lowering of KE with altitude) is exactly canceled  
by the energy separation effect caused by gravity. However he was  
only wrong with respect to gases that follow Maxwell’s distribution.


Electrical carriers in semiconductor materials are Fermions  
following Fermi-Dirac statistics and the above argument does not  
apply to them. When subjected to a voltage they do develop a  
temperature gradient. This temperature differential is hard to  
observe because it is promptly shorted by heat phonons. As  
experiments at Caltech have shown (see my papers), it can be  
observed in certain circumstances such as in high Z thermoelectric  
materials in which electrical carriers and heat phonons are strongly  
decoupled. The Onsager reciprocal of the temperature differential is  
a voltage differential which has also been experimentally observed.


The two papers above describe these results in detail.

In summary, quantum mechanics, in particular the Pauli Exclusion  
Principle, can be used to bypass classical mechanics in generating  
macroscopic effects violating the Second Law.

Other relevant papers:
1)  Hanggi and Wehner arXiv:1205.6894  show that any violation  
to the Uncertainty Principle would result in a violation of the  
Second Law. This does not contradict my research which shows use of  
QM to violate the Second Law.  The paper  also suggests for  
future research the reverse proposition that any violation of the  
Second Law would result in a violation of the Uncertainty Principle.  
This, if true, would contradict my research.
2)  Lloyd, Seth, http://people.physics.anu.edu.au/~tas110/Teaching/Lectures/L5/Material/Lloyd06.pdf 
. This paper discusses derivation of 2nd Law from QM.


I welcome any comment or criticism that you may have.

George Levy


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