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Physical interpretation of entropy if expansion causes a state of maximum entropy? 
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#1
Nov211, 10:23 AM

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Sorry for the confusing title!
I have a question that I cannot wrap my mind around... Suppose the universe attains its state of maximum entopy (assuming maximum here also involves quantum effects such that in the end even the atoms disintegrate into photons and leptons). I understand that in order to do work there needs to be a temperature gradient( which wont be avilable) but would'nt quantum fluctuations still persist (uncertainty principle)? So if you agree on the quantum effects(i hope you do) then would;nt 'we' in principle be able to measure time still? So doesn't that mean that the direction of time has nothing to do with the increase in entropy of the universe? i.e the thermodynamic arrow of time AND the cosmological arrow of time are distinct and unrelated entities??? Also...if the universe is still expanding after alls said and done...what exactly will be causing the expansion? Shouldnt it fade with the apparent dissapearance of gravitation and the dark stuff?? I' am sorry if I sound dumb but I sounded like a good idea to ask. 


#2
Nov311, 01:43 AM

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The same basic thing will eventually happen in our universe as a whole. Sure, there will still be quantum fluctuations, but they'll all average to zero. Quantum effects really don't change our understanding of time or entropy in this situation. 


#3
Nov511, 01:59 PM

P: 476

Nobody has proved that the final state of the universe was one of maximum entropy. A temperature gradient is not a needed condition for doing work. The direction of time has nothing to do with the increase in entropy of the universe. Time continues to flow when entropy is constant. And the «thermodynamic arrow of time» has nothing to see with «the cosmological arrow of time». In fact the cosmological expansion is a consequence of the field equations of GR, which is a timereversible theory that conserves entropy. 


#4
Nov511, 02:27 PM

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Physical interpretation of entropy if expansion causes a state of maximum entropy?
1. In the most simplistic view of thermodynamics, where we ignore, for instance, the chemical potential, you need either a gradient in temperature, density, or pressure in order to do work. The statement of requiring a temperature differential may not be technically correct, but the idea is more or less accurate. 2. The direction of time is exactly due to the increase in entropy of the universe. All of the microscopic laws of physics are timesymmetric, not just General Relativity. So you cannot possibly use the timesymmetric property of GR to claim it conserves entropy. Instead what happens is that the derivation of the second law of thermodynamics from statistical mechanics should be understood as stating that when you begin with a lowentropy initial condition, entropy then increases. The origin of the arrow of time, therefore, is fundamentally cosmological, because the arrow of time necessarily comes down to there being some lowentropy initial conditions for our universe. 


#5
Nov611, 05:28 AM

P: 476

Entropy has nothing to see with direction of time. Time flows the same for reversible processes. It is not true that all of the microscopic laws of physics are timesymmetric. There is wellknown irreversible microscopic formulations. E.g. By Sudarshan, By Prigogine... GR is a time reversible theory that, of course, conserves thermodynamic entropy as is wellknown. Irreversible extensions to the laws of GR are also wellknown. The derivation of the second law of thermodynamics from statistical mechanics is possible if by statistical mechanics one means some of the irreversible statistical mechanics (sometimes named nonequilibrium statistical mechanics that postulate equations beyond mechanics). If by statistical mechanics one means reversible mechanics, then the derivation is that van Kampen calls «mathematical funambulism». The claim that irreversibility is due to a lowentropy initial condition is one of the most misleading statements done about the second law and entropy that I know, and the work about the origin of the arrow of time by cosmologists (e.g. that popular book «The Quest for the Ultimate Theory of Time...») is one of the illinformed and nonsensical that I know {*}. {*} You would not be surprised that the work by this famous cosmologist has been considered pure crackpotery in wellknown blogs. 


#6
Nov611, 05:51 AM

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#7
Nov611, 08:52 AM

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#8
Nov611, 09:28 AM

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#9
Nov711, 05:18 AM

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#10
Nov711, 07:56 AM

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#11
Nov811, 06:41 AM

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P: 1,689

Just to be sure, the consensus view is given by the scholarpedia article:
http://www.scholarpedia.org/article/...'s_entropy There are still some theorists in the community that disagree with this interpretation, but it is safe to say they are in the minority. 


#12
Nov811, 08:23 AM

P: 80

I just started a new thread the other day asking "Why do so many people claim cyclic models brake down due to entropy?" There might be come good points there to better understand the roll of entropy, but I an not an expert.
I kept hearing about this arrow of time being linked to entropy from various popular sources. I vaguely remebreded doing some calculation that required entropy in a Chemical Engineering elective to pass an exam with out learning what it was, but I had an inkling that there something wasn't right about this arrow of time and entropy thing, so I simply read about entropy on wikipedia and quickly came to the conclusion that as juangra says, that entropy is incorrectly applied in this case. It didn't seem to require a post grad for me to see the problem quite quickly, but it is very interesting thinking about the reasons why you can't break the 2nd law. Judging from this thread, I can take a guess at the answer. I just learnt about the "Poincaré recurrence theorem" which can be applied to some systems which entropy can also be applied to. It shows that actually, the future will again at some point, given enough time, look very similar to the past. Entropy is relative to the observer and just tells us it will be extremely difficult for an observer to survive to see a system return to something near its start state. Perhaps entropy tells us more about the entity that is observing it, then the system its self. 


#13
Nov811, 09:47 AM

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#14
Nov811, 10:05 AM

P: 476

Moreover, claiming «consensus view» to a misguided encyclopedia article by Lebowitz reviewed by Carroll (whose contributions to the field are still less important and even considered crackpot in public by several physicists) is rather funny 


#15
Nov2711, 12:52 AM

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#16
Nov2711, 03:17 AM

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#17
Nov2811, 08:05 AM

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#18
Nov2911, 08:25 AM

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Basically, a universe where entropy cycles back and forth just doesn't work when you look at it in detail. You have to have some sort of process that can, from a highentropy state, produce a lowentropy state. One potential idea here is a quantum vacuum fluctuation: here we have a very large, highentropy state that has a fluctuation that produces a teeny tiny region of very low entropy. This isn't so dramatically unlikely any longer, because the large, highentropy state has a low entropy density, so it isn't a dramatic drop in entropy. Then, because the new state is low in entropy, it will evolve forward in time. But which direction is forward? That will be random. 


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