I am currently working on a 15 pages project about ergodicity and I wanted to include some discussion about the Poincaré Recurrence Theorem (PRT) and, as far as I know, it contradicts the 2° Law of thermodynamics in the following sense: given an initial configuration of particles, PRT states that after a long period of time they will return to the exact same positions. The problem is that this would contradict the conclusion that entropy always increases with time. I would like to know if there's a way to solve this problem, and, if there is not, what are the most accept views on this debate.
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