Note: This is a question on a particular cosmological scheme, mainly Conformal Cyclic Cosmology. In Cycles of Time, Penrose says that Black Hole Information Loss causes the entropy to decrease in a way that doesn't violate the 2nd law. I think his analysis is correct, IF it was the case that information is destroyed. But that's not the case, or at least the vast majority of the quantum gravity community doesn't think it is. So, my question is, what other things could nature do in order to make the (gravitational, as Penrose puts it) entropy decrease? Penrose seems to have in mind some alternatives, mainly --> "there volume of the phase space is infinite (i. e. there is no a maximum entropy state)". --> "gravitational degrees of freedom 'scale away' " (I don't know what he means by that) etc. I have thought of other crazy ideas, mainly: --> In an infinite time, some poincaré recurrance ought to happen in a finite time, and that would be the initial state of the next aeon. This doesn't satisfy me, because altough it could happen, one would have to choose a particular entropy value for the start of the next aeon, and that seems too arbitrary. --> The other option would be proposing that (gravitational) entropy is NOT conformally invariant, and its value significantly decreases in the "squash down" that Penrose proposes. I would be pleased if someone could clarify me the viability of this proposal.