Uncommon
Poincaré recurrence theorem
Certain dynamical systems will eventually return to (or approximate) their initial state
Poincaré recurrence theorem
In mathematics and physics, the Poincaré Recurrence Theorem states that if a system has a finite volume (or total probability measure) and preserves that volume over time, then almost every initial state will eventually return arbitrarily close to its starting position, and it will do so infinitely many times. In simple terms, it is a foundational result in both dynamical systems and statistical mechanics. The theorem is named after Henri Poincaré, who discussed it in 1890. A proof was presented by Constantin Carathéodory using measure theory in 1919.
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