Resolving the apparent contradiction between the Poincaré recurrence theorem and second law of thermodynamics I am personally a bit troubled by the apparent contradiction between second law of thermodynamics and the Poincaré's recurrence theorem. I have seen lots of arguments which seem to resolve the issue but I don't find them satisfying.
I have my own resolution of this paradox I want to propose. Please, correct me if I am mistaken. Consider an isolated system which started off with a given initial state and after the Poincaré's recurrence time it has reached arbitrarily close to the initial state we started with. But how do we know that? We only know that after we make a measurement. But that act of measurement will collapse the state to one of the eigenstates and therefore, the issue is resolved
I see this problem similar to that of the Schrödinger's cat. Is the state of the system close to the initial state after Poincaré's recurrence time is pretty much like asking whether the cat is alive or dead?
 A: Currently, the Quora question doesn't have an answer on that site:  Perhaps the one mentioned earlier has been deleted.
However, the statistical nature of the Second Law of Thermodynamics makes it a little different from other laws of physics. Quantum mechanical "unitarity" (the provision that all probabilities must add up to one) might leave Poincaré recurrences (which are relativistic) indistinguishable from QM effects, given that views about time remain rather incomplete in quantum physics:  At least since 2012, Laura Mersini-Houghton has denied that Poincaré recurrence is realistic, but has introduced a view of multiversal time as "fundamental", with passage through it (if it's possible at all) differing from passage through the "emergent" time in any of the local universes of the hypothetical multiverse concerned, which occurs in the familiar way that's limited to a single direction (that, in our locality, is always from past to future).
The problem she appears to have spotted is simply that any Poincaré recurrence might be indistinguishable from any iteration, or reiteration, of the "Many Worlds Interpretation" of quantum mechanics, that was hypothesized by Everett and explicitly endorsed by Mersini-Houghton in 2021.
The phenomenal length of the Poincaré recurrence time might make its interference with observational proof of Everett's interpretation of QM almost, but not quite entirely, hypothetical, and various cosmological models (all basically relativistic) that are each both past- and future-eternal, such as Aguirre & Gratton's "Steady-State Eternal Inflation", Nikodem Poplawski's "Cosmology with Torsion", and Nobel winner Roger Penrose's "Conformal Cyclic Cosmology", might conceivably leave that observational distinction problem which I've identified operational already:  Currently, all three of the models I've cited are described on the web, in preprints or published articles whose titles I've put within quotation marks in this paragraph.
The "observational distinction" I'm talking about would not be made by us, but it might have been made by other sentient beings (either protoplasmic, cybernetic, or hybrid) on a much larger scale of longevity in a much older civilization, and would be communicable to us, as we've already formulated the problem: There has been no evidence that extraterrestrial interventions are necessarily limited to creationists, or to deities.
