meekerdb wrote:
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. ??
No, I said you make the concept otiose by simply redefining the graining
scale at random. My comments, of course, Refer to some coherent and
consistent definition of entropy, given by a coarse-graining that is
relevant to the problem at hand.
You seem determined to play the role of 'spoiler' in this discussion,
regardless of the merit of the arguments. ;-)
Bruce
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