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This question already has an answer here:

Poincaré tell us (roughly speaking) that any hamiltonian system come up arbitrarily close to the initial condition if you wait enough time. For example, this theorem is valid for gases, and in general is one of the many key theorems that sustain Statistical Physics. And if this theorem is valid to cosmological level , what that implies?
I mean, at the end, the universe is just evolving along the most probable line which could be one posible option of many more.

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marked as duplicate by ACuriousMind Jan 26 '17 at 14:19

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    $\begingroup$ Poicare's reciprocity theorem contradicts the 2nd law of thermodynamics. $\endgroup$ – Lelouch Jan 26 '17 at 4:05
  • $\begingroup$ @Lelouch that should be an answer $\endgroup$ – DilithiumMatrix Jan 26 '17 at 4:41
  • $\begingroup$ The theorem does not apply, for instance, in an eternally expandig universe. $\endgroup$ – user126422 Jan 26 '17 at 5:21
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    $\begingroup$ In the article linked by Lelouch in his answer below, there is a key point "The result applies to isolated mechanical systems subject to some constraints, e.g., all particles must be bound to a finite volume". We do not know if the Universe complies to such an assumption. $\endgroup$ – user130529 Jan 26 '17 at 8:16
  • $\begingroup$ See also: physics.stackexchange.com/q/255142/50583, physics.stackexchange.com/q/33772/50583 $\endgroup$ – ACuriousMind Jan 26 '17 at 14:19
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Poincare's recurrence theorem contradicts the second law of thermodynamics,which states that the entropy of an isolated system is non decreasing. The theorem suggests that a bounded dynamical system satisfying certain constraints, may return arbitrarily close to its initial state within some finite time. However, it is not necesary for all parts of a system to reach this arbitrarily close state at the same time. Physically this implies that various parts of the universe may revert back to the stages of the Big Bang after a long enough time, although the second law forbids such a situation.

For further reference,give the wikipedia article a read here

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