On 11/6/2014 9:47 PM, Bruce Kellett wrote:
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.
In your initial response you said the AoT is defined by the direction of increasing
entropy. Now you say the concept of entropy is otiose. ??
Brent
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
