Re: Entropy question

Craig Franck wrote:

> I remember reading an account of the fact that when a gas expands
> in a container entropy goes up, but when gas and dust clouds in
> space do the opposite and condense, entropy increases as well. (I
> think it was in a Roger Penrose book.)

I know enough to recognize that yours is a standard question, but not
enough to spit out the standard answer. You are asking how it is in a
gravitating system that sometimes condensed states have higher entropy
than (are more stable than) non-condensed states.

Actually this formulation is not quite right, because what we expect to
have higher entropy overall is the closed system -- as Zigoteau
mentioned. And in this regard, condensation can of course be sometimes
favored in non-gravitating systems as well -- as an isolated volume
containing some water vapor and some liquid. So I'd perhaps first
wonder if there is anything fundamentally different about the treatment
of entropy in gravitationally condensing systems and in, say, van der
Walls condensing systems. Shouldn't we be equally bemused if we have
an insulated vessel containing a condensed phase in equilibrium with
some gas?

The solution must lie in the observation that there is more than matter
in such systems ... there is energy (aside from the rest mass of the
matter). And so the overall entropy is a trade off between the
positional entropy of the mass centers and the entropy associated with
the distribution of the remaining energy; and it must happen sometimes
that the spontaneous state is driven by the invisible second term.

> Why exactly is this? From a statistical POV, I don't see how N
> number of particles know which kind of system they are participating
> in or if they are behaving in the most likely way.

Whatever the expression in the N particles, it obviously effectively
leaves out the second factor. Non-interacting ideal gasses do not
condense: gravity is an interaction.

.

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