What can science tell us about history repeating itself?

Poincaré Recurrence theorem

The Poincaré recurrence theorem states that certain finite systems
will, after a sufficiently long but finite time, return to a state very
close to the initial state.

The  Poincaré recurrence time tells you how long one should wait for the recurrence to occur.

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Now if we churn out the numbers for the universe, the Poincaré recurrence time comes out too be this special number:

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If we abstract ourselves from the possibility of experimentally testing it out, the key takeaway from this is that the Poincaré recurrence time is a finite number and one does not need to wait forever to observe the recurrence of events in the universe.

Therefore in Physics it does not make any physical sense to talk beyond this time scale.

Great question! Thanks for asking!