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Assume "The Big Crunch" scenario (the universe will collapse to a singularity). In this case, I think of the entire universe as an isolated system; in the "Big Crunch" scenario, it seems to me gravity itself would act as the "walls" of the system, keeping all the matter and energy inside. Thus, by the second law of thermodynamics, entropy will increase. However, it seems to decrease (everything is being smashed together).

I know black holes get around this through the emission of Hawking radiation, but this is the emission of radiation from black holes to the universe. In the big crunch scenario, by definition, there is no universe for the radiation to escape to because the universe itself is collapsing, taking all radiation with it.

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  • $\begingroup$ An interesting book on the role of entropy in the evolution of the universe: From Eternity to Here. $\endgroup$ – rob Jun 14 '14 at 23:11
  • $\begingroup$ Related, though not a duplicate: How does the evolution of a solar system not break the second law of thermodynamics? $\endgroup$ – John Rennie Jun 15 '14 at 10:11
  • $\begingroup$ Huw Price discussed this subject in depth in his 1996 book Time's Arrow and Archimedes' Point (prce.hu/w/TAAP.html). Price argues that entropy must indeed decrease in a big crunch, because it is the time reverse of a big bang, in which entropy increases. Note, however, that due to more recent observations the expansion of the universe is now thought to be accelerating (the cause of which is unknown but is referred to as "dark energy"), so it is no longer thought that a big crunch will occur. (This does not resolve the question, however!) $\endgroup$ – Nathaniel Jun 16 '14 at 4:15
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In my opinion (which is certainly not mainstream, but which can be valid as an answer), is that there is a big contradiction here and usually this is quasi-resolved in Big Crunch arguments by assuming or even postulating additional principles.

First of all there is a big mis-understanding (or maybe mis-representation) of the 2nd Law (a suggestion: the work of I.Prigogine, for example "From Being to Becoming" and also the book "Generalised Thermodynamics" by Keenan,Hatzopoulos). These references actually state very general forms of the 2nd Law (which make apparent the restricted formulation in popular expositions and textbooks) which in fact (as one can verify experimentaly) allow forms to be created and self-organize.

The previous paragraph seeks to make justice to the 2nd Law.

Now regarding the Big Crunch, one should remember this is a speculative hypothesis. One way to reconcile with entropy is that the crunch is not a reverse expansion (as in Big Bang). Another is that General Relativity (i.e gravity) eventually prevails as more fundamental (sth the 2nd Law assumed not to be) and so resolves any conflict in this way.

UPDATE:

Furthermore according to R. Penrose ("The Emperor's new mind"), there might be a great entropic difference between big bang and big crunch, in this sense; big bang was very low-entropic due to being extremely isotropic (anyway one could divide it, it would have very similar properties), on the other hand the big crunch although a singularity can have very high entropy if this singularity is highly irregular (e.g non-isotropic etc..) (ref. "The Arrow of Time").

UPDATE2:

There is some philosophical debate whether time is an "illusion" or a "real thing", The debate revolves around SR (Minkowski space-time world geometry) and more recently around GR (Goedel's solutions to GR, thermodynamics as invariant clocks in GR etc..). See this paper on Temporal Arrows in Space-Time (and references therein) which discusses these issues and points also to questions about thermodynamics, big bang and big chill/big crunch

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