Is Poincare' Recurrence Theorem (PCRT) considered a possible explanation for the "low entropy" initial conditions of the universe? Is the following a roughly correct paraphrasing of it? For a phase space obeying Liouville's theorem (closed, non-compress-able, non-decompress-able), the probability of the system entering the lowest probability state must be 1 over "some set" of steps (I hate to use the work infinity). Is PCRT in conflict with the Fluctuation Theorem (FT)? I am confused as to whether the "away from equilibrium" clause in the FT implies that the universe should obey the FT and is therefore in conflict with PCRT, or whether that means FT isn't relevant when thinking about the universe - which is assumed to be a closed system, in equilibrium, as far as we know. I found some old threads discussing this but I sure would appreciate some re-illumination - while I am up against this confusion. I'm also struggling with the notion of compress-ability or decompress-ability of a phase space. Is there any way for the probability of a given state to change in a Liouville (Hamiltonian?) space? If you had one extra degree of freedom like "time" and in one time step added an identical copy of some "space state" to the phase space does that count against that state's probability, does that increase the phase space volume and break Liouville's rule? Weird, possibly badly worded question I know, I can understand if it's just too much to try and answer succinctly.