On 02/06/2017 11:07, Phillip Helbig (undress to reply) wrote:
In article ,
Gerry Quinn writes:

To put it another way, the 'clumpy' states in the non-gravitational
universe have lower entropy than the smooth state, but the clumpy states
in the gravitational universe have higher entropy than the smooth state.

Imagine a clumpy universe with no gravity. It has low entropy (lower
than the smooth universe). Now G starts increasing from zero to, say,
its current value (at which point the clumpy universe has a higher
entropy than the smooth universe). At some value of G, the clumpy
universe must have the same entropy as the smooth universe (which you
say has the same entropy with or without gravity). So for this value of
G, the entropy is independent of the clumpiness.

Someone has made an error somewhere.

It is a failure of intuition rather than of physics. The apparent
paradox is because a self gravitating clump of material gets hotter as
shrinks under the influence of its own gravity. Adding gravity makes the
smooth uniform matter distribution metastable wrt perturbations.

Why should it not be independent of the clumpiness?

Because it's not. A room full of air with the same density everywhere
has higher entropy than a room with all of the air squeezed into one
corner. (In the case where gravity can be neglected. When gravity
plays a role, then the clumpier distribution has higher entropy.)

The difference is that once gravity gets involved there is potential
energy available to be released when a clump of matter collapses under
the influence of mutual gravitational attraction (gravity is always and
attractive force). The shrinking material heats up as it is compressed.

The original uniform maximum entropy state is not the lowest energy
state for the system and so it is vulnerable to collapse if density
fluctuations arise sufficient to allow self gravitating clumps.

It would behave like a short lived star collapsing in on itself and then
getting smaller and hotter as a result without any nuclear fusion to
hold it up for longer. Martin Rees describes this far better than I can
on p116 of Just 6 Numbers in the section about Gravity and Entropy.

You now have a significant temperature difference between your new
gravitational star and the background which can be used to do work.

Originally it was Lord kelvin that did the lifetime computation of a
star powered only by gravitational collapse as a means of discrediting
the very long geological timescales needed for Darwinian evolution.

--
Regards,
Martin Brown