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Roger Penrose said in "A Road to Reality" (p.701):

“There is a common view that the entropy increase in the second law is somehow just a necessary consequence of the expansion of the universe. This opinion seems to be based on the misunderstanding that there are comparatively few degrees of freedom available to the universe when it is ‘small’, providing some kind of low ‘ceiling’ to possible entropy values, and more available degrees of freedom when the universe gets larger, giving a higher ‘ceiling’, thereby allowing higher entropies."

He concludes thereby:

“There are many ways to see that this viewpoint cannot be correct. It implies for example that, in those universe models where there is a collapsing phase, the entropy necessarily starts to decrease, in violation of the second law.”

And that:

“This cannot be the correct explanation for the entropy increase; for the degrees of freedom that are available to the universe are described by the total phase space PUThe dynamics of general relativity (which includes the degree of freedom (which includes the universe’s size) is just as much described by the motion of our point x in the phase space PU as are all the other physical processes involved. This phase space is just ‘there’, and it does not in any sense ‘grow with time’, time not being part of PU. There is no such ‘ceiling’, because all states that are dynamically accessible to the universe (or family of universes) under consideration must be represented in PU. It may take some while for x to reach some large coarse-graining box from some given smaller one, but the notion of an ‘entropy ceiling’ is inappropriate.”

My question would be: how deeply are expansion and thermodynamic "forces", like most prominently entropy connected? Is Penrose right once again and if yes, how so?

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  • $\begingroup$ If the 2nd law depends on the expansion of the universe, why does it still hold in gravitationally bound systems that are not participating in the expansion? $\endgroup$ – D. Halsey Oct 9 at 23:40
  • $\begingroup$ (I) Are they really not participating at all or is it just, that they are a little bit and always locally resisting it. (Assuming Big Crunch is wrong) $\endgroup$ – SomeGuy Oct 10 at 19:19
  • $\begingroup$ (II) I didn't assume, that it depended on it. I might suppose, that they both have the same origin $\endgroup$ – SomeGuy Oct 10 at 19:20
  • $\begingroup$ Related reading: Section 2.3 in plato.stanford.edu/entries/time-thermo $\endgroup$ – D. Halsey Oct 10 at 23:52
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I think Penrose is just trying to use some logic to contradict the common view. My problem with his logic is that the premise is the conclusion. If the entropy increase is caused by the expansion of the universe, then in a universe model where there is a collapsing phase, perhaps entropy will no longer increase and actually start to decrease. I’m not saying this is a valid theory, I’m just saying that our “laws” of physics are only laws because we observe them. When he says “in violation of the second law,” he is using the conclusion as the premise. The common view makes the second law the conclusion from the premise that the universe is expanding. If you change the premise to be that universe is contracting, you can’t use the prior conclusion to contradict the prior premise... it makes no sense.

Who is to say that if the universe starts contracting that entropy doesn’t flip? Certainly not me, but it’s interesting to think about and perhaps that is what Penrose wants us to contemplate.

I once had a physics professor explain entropy by spilling his soda on his desk. He asked us if the molecules of soda will ever be able to fully return to his cup. We all agreed that it’s impossible. He said that’s because entropy is always increasing. But what if when the universe starts contracting, his soda molecules start to return to his cup? If you think this sounds ridiculous, and that regardless of the expansion or contraction of the universe you wouldn’t expect the soda to return to the cup, then you probably agree with Penrose that there might not be a connection in that sense.

It’s perhaps more likely that, the expansion of the universe isn’t the premise, but the conclusion. That it is one of the results of the entropy increase, rather than the cause. The universe is the soda spilling out of the Big Bang cup.

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  • $\begingroup$ As to answer @TomA So you're just saying that his view is depending on de.wikipedia.org/wiki/Big_Crunch with or without the g-force in play. But I still am not sure, whether you / he is right even without that idea. The classical entropy as defined by boltzmann and many others is in itself not relying on any phase space, is it? It's not a diff. equation, but just a like: counting of microstates... $\endgroup$ – SomeGuy Oct 10 at 19:25

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