On 07.02.2012 23:06 Russell Standish said the following:
On Tue, Feb 07, 2012 at 08:15:10PM +0100, Evgenii Rudnyi wrote:
Russell,
This is circular - temperature is usually defined in terms of
entropy:
T^{-1} = dS/dE
This is wrong. The temperature is defined according to the Zeroth
Law. The Second Law just allows us to define the absolute
temperature, but the temperature as such is defined independently
from the entropy.
This is hardly a consensus view. See
http://en.wikipedia.org/wiki/Temperature for a discussion. I don't
personally have a stake in this, having left thermodynamics as a
field more than 20 years ago.
You are right there are different approaches. You may want for example
look at
Teaching the Second Law
http://mitworld.mit.edu/video/540
Different people, different options.
But I will point out that the zeroth law definition is limited to
equilibrium situations only, which is probably the main reason why
entropy is taken to be more fundamental in modern formulations of
statistical mechaanics.
I am not sure I understand the problem here. First one defines a
temperature for thermal equilibrium between two subsystems. Yet, after
that it is not a big deal to introduce a local temperature and the
thermal field.
dependent. As far as I remember, you have used this term in
respect to informational capacity of some modern information
carrier and its number of physical states. I would suggest to
stay with this example as the definition of context dependent.
Otherwise, it does not make much sense.
It makes just as much sense with Boltzmann-Gibbs entropy. Unless
you're saying that is not connected with thermodynamics
entropy..
Unfortunately I do not get your point. In the example, with the
information carrier we have different numerical values for the
information capacity on the carrier according to the producer and
the values derived from the thermodynamic entropy.
It sounds to me like you are arguing for a shift back to how
thermodynamics was before the Bolztmann's theoretical understanding.
A "back-to-roots" movement, as it were.
I would like rather to understand the meaning of your words.
By the way at the Boltzmann time the information was not there. So why
before Boltzmann?
I still do not understand what surface effects on the carrier has
to do with this difference. Do you mean that if you consider
surface effects you derive an exact equation that will connect the
information capacity of the carrier with the thermodynamic
entropy? If yes, could you please give such an equation?
Evgenii
Why do you ask for such an equation when the a) the situation being
physically described as not been fully described, and b) it may well
be pragmatically impossible to write, even though it may exist in
principle.
This seems like a cheap rhetorical trick.
As I have mentioned, I would like to understand what you mean. In order
to achieve this, I suggest to consider simple problems to apply your
theory. I think it is the best to understand a theory by means of simple
practical applications. Why do you consider this as a chip rhetorical trick?
What I observe personally is that there is information in informatics
and information in physics (if we say that the thermodynamic entropy is
the information). If you would agree, that these two informations are
different, it would be fine with me, I am flexible with definitions.
Yet, if I understand you correctly you mean that the information in
informatics and the thermodynamic entropy are the same. This puzzles me
as I believe that the same physical values should have the same
numerical values. Hence my wish to understand what you mean.
Unfortunately you do not want to disclose it, you do not want to apply
your theory to examples that I present.
Evgenii
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