Thermodynamics and the Big Crunch

[Enola Straight]

Does the Big Crunch...one possible end of the universe...violate Thermodynamics?

Does "all space, time, matter, and energy contracted into one neat orderly geometric point" violate "entropy always increases in the universe as a whole"?

[Eris]

Interestingly enough it does, sort of. From what I understand, and keep in mind this is coming from the point of view of a chemist, not a cosmologist, if we started contracting the second law would reverse itself, and entropy would always decrease. In such a world time's arrow, to use a popular phrase, would flip and you start getting really funky results. All product-favoured reactions would become reactant-favoured, and visa versa; und so weiter.

I'm sure there are many on the board that could give you a better idea about it than me, though.

[metavac]

Does "all space, time, matter, and energy contracted into one neat orderly geometric point" violate "entropy always increases in the universe as a whole"?

Not an easy question to answer. A gravitational singularity is the maximum entropic state an isolated, universe dominated by positive mass-energy can achieve. Things become significantly more complex with other geometries, especially ones that apply to a universe like ours where expansion seems to be accelerating. That's one half of the reason why there are no thermodynamic laws that apply globally across the large scale structure of the universe.

[Kuroneko]

Going by Penrose's treatment of gravitational entropy [*], in the idealized Friedmann-Robertson-Walker family of models (including the 'big crunch' scenario, of course), there is no change in gravitational entropy at any point in time--and since the models assume homogeneity, no change in thermodynamic entropy either.

However, for an inhomogeneous collapse, as would be more physically realistic, the picture is a bit different. In general, gravitational collapse tends to increase gravitational entropy (up to the maximal entropy of a black hole), but the thermodynamic entropy, and therefore overall entropy, would be more complicated. It will tend to decrease due to increases in density and inhomogeneity, but the collapse will also raise the temperature, thus increasing the entropy. I'm not sure how these effects stack up against one another, but I'm fairly confident that overall entropy will still increase during the big crunch phase of a closed universe.

If I recall correctly, Hawking held both positions at different points in time. But I don't know his reasons.

[*] Which I'm not too clear on, but since he identifies it with the Weyl curvature somehow, and the Weyl tensor vanishes in all FRW solutions, the following is a safe statement.

[Ariphaos]

Wouldn't entropy begin to decrease as Planck temperature was approached?

[Dark Hellion]

In a big crunch scenario, as the universe shrunk the energy density would increase, matter breaking down under the extreme temperature into QGP and finally a few seconds before the universe decided to "go pop" even quarks would be unable to exist. However, entropy might be able to reverse towards the end, when the universe is small enough to experience quantum mechanical phenomena over the entirety of itself. Given the time scale there may be able to be an entropy reversal however the whole university going into a singularity is reaching a max state of entropy IIRC.

The bigger problems are of course going to be the multi-billion degree background temperature and clouds of relativistic plasma. I think entropy would be the least of our concerns.

[Redleader34]

Can't one use these conditons for making a trans universal supercomputer, or something of that nature?

[Kuroneko]

Wouldn't entropy begin to decrease as Planck temperature was approached?

Why? The entropy of a homogeneous collapse is actually constant--both gravitational and thermodynamic entropies are constant, actually. Inhomogeneity will tend to increase gravitational entropy, and while its effect on thermodynamic entropy is not as straightforward, I don't see any particular reason for it to decrease even under that condition. Perhaps you are thinking of some kind of 'entropy acceleration' or some-such.

[metavac]

Why? The entropy of a homogeneous collapse is actually constant--both gravitational and thermodynamic entropies are constant, actually. Inhomogeneity will tend to increase gravitational entropy, and while its effect on thermodynamic entropy is not as straightforward, I don't see any particular reason for it to decrease even under that condition. Perhaps you are thinking of some kind of 'entropy acceleration' or some-such.

This doesn't sound right. The entropy of a gravitationally bound system should decrease as it collapses, increasing the entropy of the surrounding space with waste heat. Hell, that's what black hole thermodynamics predict unless I've missed something.

[Kuroneko]

This doesn't sound right. The entropy of a gravitationally bound system should decrease as it collapses, increasing the entropy of the surrounding space with waste heat. Hell, that's what black hole thermodynamics predict unless I've missed something.

That's almost the opposite of what black hole thermodynamics predicts. Black holes are maximally entropic for their surface area, not minimally as you suggest. Perhaps you're confused by the fact that gravitationally bound systems have negative heat capacities--they decrease in temperature as one gives them energy. For black holes, it's very clear from the equation for Hawking temperature, but it is true for general collapse scenarios (e.g., stellar formation).

Edit: Oh, I see. You're thinking of an already-formed black hole radiating away and decreasing its entropy. That's definitely not the situation here. Think instead of the gravitational collapse of the matter that formed the black hole. Black hole thermodynamics predicts that the formation of the black hole will increase the entropy of the system, and indeed will have maximal entropy for any given total energy of the system.

[Ariphaos]

Why? The entropy of a homogeneous collapse is actually constant--both gravitational and thermodynamic entropies are constant, actually. Inhomogeneity will tend to increase gravitational entropy, and while its effect on thermodynamic entropy is not as straightforward, I don't see any particular reason for it to decrease even under that condition. Perhaps you are thinking of some kind of 'entropy acceleration' or some-such.

No, I mean, once a system starts approaching planck temperature (as would seem to be happening in a collapse scenario), wouldn't the variance in individual particle energy must get less and less, reducing the number of possible states and thus entropy?

[Kuroneko]

No, I mean, once a system starts approaching planck temperature (as would seem to be happening in a collapse scenario), wouldn't the variance in individual particle energy must get less and less, reducing the number of possible states and thus entropy?

There's the problem of not being able to tell them apart under those conditions. Another way to think of this is that at those temperatures the particles will tend to form black holes themselves, which are maximally entropic.

[metavac]

Edit: Oh, I see. You're thinking of an already-formed black hole radiating away and decreasing its entropy. That's definitely not the situation here. Think instead of the gravitational collapse of the matter that formed the black hole. Black hole thermodynamics predicts that the formation of the black hole will increase the entropy of the system, and indeed will have maximal entropy for any given total energy of the system.

You know, I can actually buy this. The early universe should be to an absurd degree more conformally flat than today in order to produce the homogeneity and isotropy of the universe today, so the Weyl tensor would vanish back toward t = 0. Likewise, clumping of matter should steadily increase the Weyl tensor over time. If black holes are maximally entropic for their area and are the penultimate clumps of matter, it makes sense that the Weyl tensor be viewed as a measure of entropy. Oh, and the Big Crunch accompanies everything clumping back together, but conformal flatness is recovered by the final black hole state radiating away. So the sum of gravitational and thermodynamic entropy should be constant, right?

[Kuroneko]

It should be noted that all of this is still speculative on several levels; for one, the relationship between the Weyl tensor and gravitational entropy (density) is a matter of conjecture and is not well-established. A common definition is that its square is the ratio of the Weyl scalar and the Ricci scalar, but the more recent proposal of the Kretschmann scalar instead is probably more appropriate.

The early universe should be to an absurd degree more conformally flat than today in order to produce the homogeneity and isotropy of the universe today, so the Weyl tensor would vanish back toward t = 0.

Right. And if it was perfectly homogeneous, then the Weyl tensor would vanish at all times. But of course that's not what actually happened.

Likewise, clumping of matter should steadily increase the Weyl tensor over time. If black holes are maximally entropic for their area and are the penultimate clumps of matter, it makes sense that the Weyl tensor be viewed as a measure of entropy.

Indeed. Penrose first noticed the similarity about three decades ago.

Oh, and the Big Crunch accompanies everything clumping back together, but conformal flatness is recovered by the final black hole state radiating away.

Er, either you're colliding two trains of thought there, or this isn't quite right. Conformal flatness is recovered with an isolated black hole radiating away, but that's not what happens in a Big Crunch scenario. We can expect a Big Crunch to be highly non-uniform for a realistic universe, and only exaggerate the inhomogeneities during its final moments, which would mean gravitational entropy should not decrease.

So the sum of gravitational and thermodynamic entropy should be constant, right?

I doubt that that's possible outside of highly idealized conditions (e.g., perfect homogeneity, in which case they stay constant even individually). A gravitationally collapsing gas should increase in both gravitational entropy and thermodynamic entropy. The former is obvious if gravitational entropy is identified with Weyl curvature somehow, although the latter is obvious because there are competing effects of raised density and temperature.

Hmm... come to think of it, the latter is an interesting problem.

[metavac]

Er, either you're colliding two trains of thought there, or this isn't quite right. Conformal flatness is recovered with an isolated black hole radiating away, but that's not what happens in a Big Crunch scenario. We can expect a Big Crunch to be highly non-uniform for a realistic universe, and only exaggerate the inhomogeneities during its final moments, which would mean gravitational entropy should not decrease.

Right, because we'd never see black holes clump together (they'd radiate away in a finite amount of time but their approach would continue towards infinity). On the other hand, in a finite amount of time all black holes will have radiated away, which means gravitational entropy should be decreasing and the Weyl tensor vanishing again. Is this not so?

I doubt that that's possible outside of highly idealized conditions (e.g., perfect homogeneity, in which case they stay constant even individually). A gravitationally collapsing gas should increase in both gravitational entropy and thermodynamic entropy. The former is obvious if gravitational entropy is identified with Weyl curvature somehow, although the latter is obvious because there are competing effects of raised density and temperature.

Hmm... come to think of it, the latter is an interesting problem.

Thermodynamic entropy should decrease with an increase in temperature...a clumping gas should basically tend away from thermal equilibrium with its environment, right? Ah, but since potential energy falls faster than kinetic energy increases, the sum of the two shouldn't be constant. I get it.

[Kuroneko]

Retroactive edit: "the latter is not obvious". Typo--apologies. I was trying to say that it's not trivial because one effect decreases entropy while another increases it.

Right, because we'd never see black holes clump together (they'd radiate away in a finite amount of time but their approach would continue towards infinity).

No; black holes in collision would merge in finite time.

On the other hand, in a finite amount of time all black holes will have radiated away, which means gravitational entropy should be decreasing and the Weyl tensor vanishing again.

That's true for isolated black holes, yes.

Thermodynamic entropy should decrease with an increase in temperature...a clumping gas should basically tend away from thermal equilibrium with its environment, right?

Yes, but thermodynamic entropy actually increases with increasing temperature. It decreases with increasing density, however--that's why I said they were competing effects.

I'll try to see how it behaves exactly later.