CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search In mathematics , the Poincaré recurrence theorem states that certain systems will, after a sufficiently long but finite time, return to a state very close to 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 published it in 1890. 1 Precise formulation 2 Discussion of proof 3 Formal statement of the theorem 3.1 Theorem 1 3.2 Theorem 2 4 Quan...