# Is large-scale “time reversal” (Poincaré recurrence) possible given infinite time?

The following are some assumptions I'm basing my question on, from what (little) I understand of physics. I list them so an expert can (kindly) tell me where I'm going wrong.

• There is a probability assigned to every possible sequence of events.
• Besides sequences that violate the "rules", every sequence seems to have a nonzero probability.
• This applies to large scale systems as well, except the odds usually seem to tend toward nearly 100% in favor of certain sequences (i.e., paths of highest entropy).
• There is therefore a probability assigned to the following sequence of events: a system (large or small scale) reversing everything it's done since a certain point in time (Poincaré recurrence), and ending up back "almost" where it started; perhaps not an exact copy.
• The universe appears to be expanding, and for all we know will do so forever, possibly leading to the heat death of the universe.

Here's my question:

Assuming the universe will continue on forever (and therefore that we have infinite time in our equations), isn't there a nonzero probability that everything in it can "reverse" itself and end up back at the big bang, perhaps in a somewhat slightly altered path?

Is dark energy is the only thing preventing this? If so, (1) would this be possible without dark energy? (2) could the force carriers, assuming they exist, behind dark energy obey quantum mechanics, and therefore be "time reversable"?

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Given that nobody knows the equation that universe follows its not possible to give a definitive answer to your question. However this question has been studied for some 'simple' systems. See for example Poincare recurrence theorem. –  user10001 Aug 9 '12 at 15:59
Thank you, your link to Poincaré recurrence useful and relevant. Where I said "time reversal", I really could say "poincare recurrence". I've updated the question to mention Poincaré recurrence, since, in a nutshell, I'm really asking "Does Poincaré recurrence apply to the entire universe?" –  Jay Aug 12 '12 at 15:46