KnowraPoincaré recurrence theoremLinked fromLinked fromThe 13 pages that link to Poincaré recurrence theorem, each with the reason it gives.All 13Broader topic 1Related 6Compared with 6Henri PoincaréBroader topic: Poincaré used recurrence to establish a general property of conservative mechanical systems.Second law of thermodynamicsCompared with: Recurrence raises questions about how statistical entropy increase coexists with reversible microscopic dynamics.Irreversible processCompared with: Recurrence complicates claims that microscopic evolution is permanently one-way.Joseph LiouvilleCompared with: It concerns recurrence in dynamics, while Liouville’s theorem concerns preservation of phase-space volume.Ergodic hypothesisRelated: Recurrence constrains trajectories but does not by itself establish ergodicity.Ergodic theoryRelated: It establishes recurrence without requiring detailed knowledge of a system's equations.KAM theoryRelated: It offers a distinct route to recurrent behavior, without requiring persistent quasiperiodic tori.Loschmidt's paradoxCompared with: It raises a related challenge to permanent entropy growth, but concerns long-term recurrence rather than reversed trajectories.Boltzmann brainRelated: Recurrences provide one route by which extraordinarily rare configurations can eventually appear.Hamiltonian systemRelated: Finite-volume Hamiltonian systems satisfy recurrence under suitable conditions.Kolmogorov–Arnold–Moser theoremCompared with: Recurrence is a broad measure-theoretic result, while KAM identifies specific persistent quasiperiodic structures.Ergodic theoremRelated: It is a complementary long-term result derived from measure preservation.Poincaré–Birkhoff theoremCompared with: Recurrence concerns near returns, while the annulus theorem forces exact fixed points.