Re: Entropy confusion, please help!

Uno Lapideus <henry@xxxxxxxxxxxxxxxxxxxx> wrote:

[...]
At the root of my confusion is the supposed "running down" of the
post-inflationary extremely uniform "energy vapor" (at least that is
what I understand from reading about various interpretations of current
CMB measurements)... If this state of affairs represented "high
entropy," would not the current state of the Universe have even higher
entropy? That is, being more disordered... Galaxies, to my eyes, look
pretty well ordered, if not uniformly distributed (which, again to my
thinking, they ought to be, given the extreme uniformity of the
"starting point")...

Part of the problem is that the picture of entropy as "disorder,"
while sometimes useful, can also be misleading. "Order" here has
a technical meaning -- it is, roughly, a count of the number of
microscopic physical states that can give the same macroscopic state
-- and it may not have much connection to our intuitive picture of
what looks "orderly."

In this particular case, a galaxy certainly seems more ``ordered''
than a cloud of gas. But if you sit down and do the calculation
you'll find that the actual entropy of a group of stars (plus the
radiation emitted during the gravitational collapse of the cloud
of gas) is *greater* than the entropy of the cloud before collapse.
This is a consequence of some very counterintuitive features of
self-gravitating systems: for example, they have negative heat
capacities, so the flow of heat from hot areas to cold areas leads
to increasing inhomogeneity (``lumpiness''). If you insist on
thinking of entropy as ``disorder,'' you're stuck with a picture
in which a star or a galaxy is less orderly than a diffuse cloud of
gas.

For the spherically symmetric case (a star rather than a whole
galaxy), the calculation was first done by Antonov, published in
Vest. Leningrad Univ. 7 (1962) 135; there's a translation in IAU
Symposium 113 (1995) 525. The computation was repeated and
elaborated by Lynden-Bell and Wood, Mon. Not. R. Astr. Soc.
138 (1968) 495. There's a nice summary in a talk by Lynden-Bell,
which you can obtain at http://arXiv.org/abs/cond-mat/9812172 .
For a quick reference, see the beginning of chapter 5 of Zeh's
book _The Physical Basis of the Direction of Time_.

Steve Carlip
.

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