I've read around a bit, and it seems to be universal that the notion of a Poincare recurrence time for the universe exists. And it seems to be debated that the universe can be given an entropy, as it is contested whether or not it can be viewed as a closed system.

Something about this argument makes me think that the notion of a Poincare recurrence time for the universe also can't exist. Would this depend on the universe being a closed or static system?

  • $\begingroup$ I have changed the title, since this is a specific question about the Poincare recurrence time of the Universe, not a general question about the Poincare recurrence time. $\endgroup$ – Mark Mitchison May 10 '16 at 17:31

Poincaré theorem holds for Hamiltonian systems of finite phase space. We do not know whether Universe is finite or infinite and thus whether it is better to describe it with mechanical model of finite or infinite phase space.

  • $\begingroup$ Moreover, note that the entropy remains a useful concept even when Poincaré recurrence holds (for large systems, of course). $\endgroup$ – Yvan Velenik May 10 '16 at 17:13
  • $\begingroup$ We don't even know if the universe is a Hamiltonian system. Even if it is, the recurrence time of the quantum mechanical version is a questionable concept, since it is not clear how one can measure the wave function of the universe (without disturbing it, at that!). $\endgroup$ – CuriousOne May 10 '16 at 20:49

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