{"slug":"school-zermelo-poincar-recurrence-objection","verification":{"valid":true,"entries":3,"head":"6c0c141b2eaacaa9d5720d0c21d6c9423c4d5d536262814407e9b53a2922c2c0"},"count":3,"sources":[{"id":"s1","type":"other","url":"https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theorem","title":"Poincaré recurrence theorem","quote":"The theorem is named after Henri Poincaré, who discussed it in 1890.","summary":"Standard reference confirming Poincaré's 1890 statement of the recurrence theorem.","claim_ids":["c1"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-09T06:52:10.687Z","link_status":"ok","quote_status":"unverified","prev":"genesis","hash":"d17d03dbb573d9e0b53d1a37e2cfbfe4f8630c7a31def117439f21cbf840013e"},{"id":"s2","type":"other","url":"http://ui.adsabs.harvard.edu/abs/1983AmJPh..51..894S/abstract","title":"Zermelo, Boltzmann, and the recurrence paradox","quote":"The papers exchanged by Ludwig Boltzmann and Ernst Zermelo concerning the recurrence paradox are summarized.","summary":"Historical summary of the 1896 Zermelo-Boltzmann exchange.","claim_ids":["c2"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-09T06:52:10.687Z","link_status":"ok","quote_status":"unverified","prev":"d17d03dbb573d9e0b53d1a37e2cfbfe4f8630c7a31def117439f21cbf840013e","hash":"9053135c353b50e9c8319327a9db078e95c6f75f31e15dd6b7fddab1c0658820"},{"id":"s3","type":"other","url":"https://www.sciencedirect.com/science/article/abs/pii/S1355219809000124","title":"Boltzmann's H-theorem, its discontents, and the birth of statistical mechanics","quote":"A comparison is made of the traditional Loschmidt (reversibility) and Zermelo (recurrence) objections to Boltzmann's H-theorem.","summary":"Discusses the scale of recurrence times and physical applicability.","claim_ids":["c3"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-09T06:52:10.687Z","link_status":"http_403","quote_status":"unverified","prev":"9053135c353b50e9c8319327a9db078e95c6f75f31e15dd6b7fddab1c0658820","hash":"6c0c141b2eaacaa9d5720d0c21d6c9423c4d5d536262814407e9b53a2922c2c0"}]}