entropy and gravitation

A smooth distribution corresponds to high entropy and a lumpy one to low
entropy if gravity is not involved. For example, air in a room has high
entropy, but all the oxygen in one part and all the nitrogen in another
part would correspond to low entropy.

If gravity is involved, however, things are reversed: a lumpy
distribution (e.g. everything in black holes) has a high entropy and a
smooth distribution (e.g. the early universe) has a low entropy.

Let's imagine the early universe---a smooth, low-entropy
distribution---and imagine gravity becoming weaker and weaker (by
changing the gravitational constant). Can we make G arbitrarily small
and the smooth distribution will still have low entropy? This seems
strange: an ARBITRARILY SMALL G makes a smooth distribution have a low
entropy. On the other hand, it seems strange that the entropy should
change at some value of G.

On 30 May 2017 Phillip Helbig wrote:
it seems strange that the entropy should change at some value of G.

For a while I thought thermodynamics was the most marvellous science,
but now I think that "entropy" is just a fudge to fill in the gap
after the enthalpy is measured. So who ever proved that "disorder" is
a full explanation of so-called entropy? I had the same thoughts as
Phil about the effects of scale on that interpretation (as well as how
it is different in space than on a planet), but casting it in the
light of the value of G is a new one.

On 5/30/2017 6:55 AM, Phillip Helbig (undress to reply) wrote:
A smooth distribution corresponds to high entropy and a lumpy one to low
entropy if gravity is not involved. For example, air in a room has high
entropy, but all the oxygen in one part and all the nitrogen in another
part would correspond to low entropy.

If gravity is involved, however, things are reversed: a lumpy
distribution (e.g. everything in black holes) has a high entropy

But if everything is in one big black hole, and the black hole
would need only mass and angular momentum and charge to describe
it, then that would be extremely low entropy (and essentially we
would have back the "ordinary" behavior you described first).

So the difference is only in the entropy that is in the "soft
supertranslation hair" (if that is the correct theory..)

If the oxygen in one corner of the room would also have this
extra entropy that black holes seem to have (for whatever reason),
then the cases would be the same.

Provided of course that before black hole formation occurs
the normal behavior (lumpy distribution has lower entropy) is
respected by gravity as it is by other forces. So the question
is: would there still be a reason, in cases without black holes,
to expect that gravity is different?

--
Jos

In article , Jos Bergervoet
writes:

But if everything is in one big black hole, and the black hole
would need only mass and angular momentum and charge to describe
it, then that would be extremely low entropy (and essentially we
would have back the "ordinary" behavior you described first).

The first clause doesn't really make sense, since if "everything"
(presumably meaning all matter in the universe) were "in one big black
hole", this would have to be something different than what is normally
thought of as a black hole, e.g. a static solution in a background of
Minkowski space.

In article ,
says...

A smooth distribution corresponds to high entropy and a lumpy one to low
entropy if gravity is not involved. For example, air in a room has high
entropy, but all the oxygen in one part and all the nitrogen in another
part would correspond to low entropy.

If gravity is involved, however, things are reversed: a lumpy
distribution (e.g. everything in black holes) has a high entropy and a
smooth distribution (e.g. the early universe) has a low entropy.

Let's imagine the early universe---a smooth, low-entropy
distribution---and imagine gravity becoming weaker and weaker (by
changing the gravitational constant). Can we make G arbitrarily small
and the smooth distribution will still have low entropy? This seems
strange: an ARBITRARILY SMALL G makes a smooth distribution have a low
entropy. On the other hand, it seems strange that the entropy should
change at some value of G.

The smooth distribution always has the same entropy. Start with the
smooth distribution and no gravity, and increase the gravitational
constant. Now high entropy states start to become available that were
not available withouy gravity.

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.

The clumpiness versus dispersion 'paradox' isn't such a paradox either.
When gravitational clumping takes place, energy is released which will
eventually become widely dispersed as low-grade thermal energy. This
ultimately applies even if black holes are formed, although the thermal
energy will for a long time be locked up in black holes.

- Gerry Quinn

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In article ,
Gerry Quinn writes:

The smooth distribution always has the same entropy. Start with the
smooth distribution and no gravity, and increase the gravitational
constant. Now high entropy states start to become available that were
not available withouy gravity.

Sounds plausible.

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.

In article ,
says...

In article ,
Gerry Quinn writes:

The smooth distribution always has the same entropy. Start with the
smooth distribution and no gravity, and increase the gravitational
constant. Now high entropy states start to become available that were
not available withouy gravity.

Sounds plausible.

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?

Consider a smooth universe full of hydrogen, with non-zero density and
no gravity. This universe is clumpy too, it's just that the clumps are
mostly H2.

You could make the same paradox by imagining a universe full of H atoms,
and slowly turning on atomic interactions.

- Gerry Quinn

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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.)

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

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