entropy and gravitation

Am 02.06.2017 um 12:07 schrieb Phillip Helbig (undress to reply):
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.

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.)


This kind of comparison needs a gas, a process that is adiabatic for one
leg and isothermal for the other leg of a reversible path in state spece
and therefor at least one thermal bath.

Because all such things do not exist in the universe of lets say a gas
of galaxies or photons or hydrongen and helium all kinds of modelling of
entropy along the classical examples of gas in a variable volume and and
two temperatur baths at hand are highly doubted in the community.

Finally, the two volumes of a system at two times are the 3d-boundaries
of a 4-volume, bottom and ceiling orthogonal to the direction of time.

With a nonstationary 3-geometry in the rest system volume changing has
no thermodynamic effect because all particles and fields follow their
unitary or canonically free time evolution in a given Riemann space.
That does not change the von Neumann entropy because of Liouvilles
theorem of constancy of any 6-volume element of spce and momentum.

Finally for interacting system of fermionic particles and fields at
temperatures below the Fermi temperature, a state with lumpy matter and
a small fraction of free gas over its surface is the state of maximal
entropy.

Interacting matter evenly distibuted in a given volume that it does not
fully occupiy as a condensed body is highly improbable.

--

Roland Franzius