meekerdb wrote:
On 11/6/2014 9:08 PM, Bruce Kellett wrote:
LizR wrote:
(Another way to look at this is that the expansion is producing more
available states for the universe to move into, effectively raising
the entropy ceiling. This means an expanding universe can never reach
a state of equilibrium - this is particularly clear during the BB
fireball, which I would say is very near to equilibrium for a lot of
the time.)
I thought I remembered that someone had written that the idea that the
expansion produces more states so the entropy ceiling increases with
the expansion of the universe is mistaken. I have found the reference,
it is Roger Penrose in 'The Road to Reality' in Section 27.6 (p. 701ff)
He writes:
"There is a common view that the entropy increase in the second law is
somehow just a necessary consequence of the expansion of the universe.
This opinion seems to be based on the misunderstanding that there are
comparatively few degrees of freedom available to the universe when it
is 'small', providing some kind of low 'ceiling' to possible entropy
values, and more available degrees of freedom when the universe gets
larger, giving a higher 'ceiling', thereby allowing higher entropies. ...
"There are many ways to see that this viewpoint cannot be correct....
...The degrees of freedom that are available to the universe are
described by the total phase space. The dynamics of GR (which include
the degree of freedom defining the universe's size) is just as much
described by the motion of our point x in the phase space as are all
the other physical processes involved. This phase space is just
'there', and it does not in any sense 'grow with time', time not being
part of the phase space.
No, but dynamics consist of moving through phase space. Entropy is
always relative to constraints (with no constraints you just have the
micro state and entropy is zero). So relative to a given size I think
the number of states does grow with size. Penrose is right but he's
removing the constraint on size.
As I said in my other reply, that simply makes the concept of entropy
otiose in these discussions. In cosmology, by and large, we are talking
classical physics with GR. Liouville's theorem is relevant.
Bruce
Brent
There is no 'ceiling', because all states that are dynamically
accessible to the universe (or family of universes) under
consideration must be represented in this phase space....."
I recommend Penrose's book for a lucid explanation of these things.
Bruce
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