Re: Entropy confusion, please help!

carlip-nospam@xxxxxxxxxxxxxxxxxxx wrote:

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.

It is, even thermodynamically. It is the the _net_ effect including
the role of the radiation bath which is "less ordered", as you say.

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 <...>

Or not. Systems contrive to increase their overall entropy by partial
condensation all the time. Should we be more bemused by the galaxy
than we are by the condensation of steam into water droplets? Doesn't
that reduce configurational entropy?

<crank mode on>

I'll have to ghost of Feynman come back and enunciate this. _Then_
you'll stroke your chin and go "hmm...", sir!

<crank mode off>

<...> for example, they have negative heat
capacities, so the flow of heat from hot areas to cold areas leads
to increasing inhomogeneity (``lumpiness'').

The flow of heat from hot areas to cold areas increases the entropy of
the cold area and decreases the entropy of the hot area, but always
increases the entropy of the cold area more. That's why the heat flows
in the first place. Spontaneous condensation follows a similar
calculus, with decrease in configuration entropy taking the place of
decrease in entropy of the hot side.

I'm not sure what this has to do with "negative heat capacity".

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.

Possibly true, but a different semantic problem than the one just
addressed.

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_.

One might draw the impression from your citations that this is some
effect peculiar to the condensation of stars and galaxies, whereas the
overall accounting is analogous to the condensation of water on your
windowpane. Chiefly there is a difference of scale, with gravity
taking the role of the attractive portion of the intermolecular
potentials. Not as impressive, and so mundane.

I'm not sure any of this directly addresses the OP's question, though.

.

Relevant Pages

  • Re: Entropy confusion, please help!
    ... post-inflationary extremely uniform "energy vapor" (at least that is ... entropy," would not the current state of the Universe have even higher ... than a cloud of gas. ... For the spherically symmetric case (a star rather than a whole ...
    (sci.physics)
  • Re: Entropy confusion, please help!
    ... entropy," would not the current state of the Universe have even higher ... than we are by the condensation of steam into water droplets? ... increases the entropy of the cold area more. ... That's why the heat flows ...
    (sci.physics)