Poincaré recurrence theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-29

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theorem


00:00:48 1 Precise formulation
00:01:28 2 Discussion of proof
00:04:56 3 Formal statement of the theorem
00:05:33 3.1 Theorem 1
00:07:29 3.2 Theorem 2
00:08:13 4 Quantum mechanical version
00:13:25 5 See also



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SUMMARY
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In physics, the Poincaré recurrence theorem states that certain systems will, after a sufficiently long but finite time, return to a state very close to, if not exactly the same as, the initial state.  The Poincaré recurrence time is the length of time elapsed until the recurrence; this time may vary greatly depending on the exact initial state and required degree of closeness. The result applies to isolated mechanical systems subject to some constraints, e.g., all particles must be bound to a finite volume. The theorem is commonly discussed in the context of ergodic theory, dynamical systems and statistical mechanics.
The theorem is named after Henri Poincaré, who discussed it in 1890 and proved by Constantin Carathéodory using measure theory in 1919.