Standard view on Big Bang is that it has started with a perfect point, followed be faster-than-light inflation. This initial perfect point does not seem to agree with CPT symmetry, which is generally believed to be fundamental in physics, and suggests that there was something before this initial point.
This takes us to alternative: also quite popular cyclic model, saying that there was some gravitational collapse before - Big Bounce: Big Crunch, immediately followed by our Big Bang. Assuming our Universe will finally collapse, there can be a cycle of crunch-bang, evolution. One might criticize that we "know" that universe expansion is accelerating. But it is believed to be pushed away by "dark energy", so accordingly to energy conservation, its strength should decrease with $R^3$ volume, while attracting gravity weakens like $1/R^2$ and so should finally win - leading to collapse.
Anyway, it seems there is a problem with the second law of thermodynamics in cyclic universe hypothesis - on one hand entropy is believed to be always increasing into our future, on the other Big Bangs should intuitively 'reset the system' - start new entropy growth from minimum - similar for successive Big Bangs (?)
So I wanted to collect some possible answers to this question and ask for the proper one - here is a schematic picture of the basic ones (to be expanded):
The age of thermal death means that there are nearly no changes because practically everything is in thermal equilibrium, most of stars have extinguished.
1) The 2nd law is sacred - successive Big Bangs have larger and larger entropy,
2) It is possible to violate 2nd law, but only during the Great Bounce,
3) It is possible to violate 2nd law in singularities like black holes - the universe may be already in thermal death, while the entropy slowly "evaporate" with black holes (I have heard such concept in Penrose lecture in Cracow),
4) The second law of thermodynamics is not fundamental, but effective one - physics is fundamentally time/CPT symmetric. So Big Bounce is not only single Big Bang, but from time/CPT symmetry perspective, there is also second BB-like beginning of universe reason-result chain in reverse time direction. The opposite evolutions would finally meet in the extremely long central thermal death age, which would probably destroy any low-entropic artifacts.
I see 1) as a total nonsense - thermal death is near possible entropy maximum (like lg(N)).
Also 3) doesn't seem reasonable - hypothetical Hawking radiation is kind of thermal radiation - definitely not ordering energy (decreasing entropy), but rather equilibrating degrees of freedom - leading to thermalization of universe.
2) sounds worth considering - physics doesn't like discontinuities, but Big Bounce is kind of special - crushes everything, resetting the system.
And 4) seems the most reasonable, but requires accepting that thermodynamical time arrow is not fundamental principle, but statistical effect of e.g. low entropic BB-like situation: where/when everything is localized in small region.
Assuming our universe will eventually collapse, which thermodynamical scenario seems most reasonable? Why? Maybe the above list misses some crucial possibility?
And generally - what are arguments against cyclic model?