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. 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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