{"slug":"thinker-paul-ehrenfest","verification":{"valid":true,"entries":6,"head":"0e57741cdbaa2142faead6a07f37bef2109c3d67c415452bd81dd8d4607b16af"},"count":6,"sources":[{"id":"s1","type":"other","url":"https://en.wikipedia.org/wiki/Paul_Ehrenfest","title":"Paul Ehrenfest","quote":"In their influential 1911 article, Ehrenfest and Ehrenfest summarized and discussed problems with the ergodic hypothesis and then proposed instead the quasi-ergodic hypothesis.","summary":"1911 Encyklopädie article on foundations of statistical mechanics.","claim_ids":["c1"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-08T06:50:18.655Z","link_status":"ok","quote_status":"unverified","prev":"genesis","hash":"c9d419dbd96c202e146cb2795ddf66112376954665b27da712f01309a84fee20"},{"id":"s2","type":"other","url":"https://arxiv.org/pdf/1502.03022","title":"Ehrenfest's adiabatic hypothesis in Bohr's quantum theory","quote":"Paul Ehrenfest formulated and applied his adiabatic hypothesis in the early 1910s.","summary":"Details the development of adiabatic invariants 1911-1916.","claim_ids":["c2","c7"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-08T06:50:18.655Z","link_status":"ok","quote_status":"unverified","prev":"c9d419dbd96c202e146cb2795ddf66112376954665b27da712f01309a84fee20","hash":"6a2096698903c1d69199eff0f8b34547b059c6dae0f3593ea4bb048ef1c64709"},{"id":"s3","type":"other","url":"https://www.informationphilosopher.com/solutions/experiments/ergodic_hypothesis/","title":"The Ergodic Hypothesis","quote":"Paul and Tatiana Ehrenfest made the ergodic hypothesis the central question in statistical mechanics.","summary":"Covers the urn model and quasi-ergodic proposal.","claim_ids":["c3"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-08T06:50:18.655Z","link_status":"ok","quote_status":"verified","prev":"6a2096698903c1d69199eff0f8b34547b059c6dae0f3593ea4bb048ef1c64709","hash":"56281e5da405dc3b98aebe2b47e2344c9964132e11fee5959afd12127e33cead"},{"id":"s4","type":"other","url":"https://physicstoday.aip.org/features/paul-ehrenfests-final-years","title":"Paul Ehrenfest's final years","quote":"The 'Ehrenfest theorem' of 1927, relating the expectation values of quantum mechanical operators to classical Poisson brackets.","summary":"Reference to the 1927 theorem.","claim_ids":["c4"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-08T06:50:18.655Z","link_status":"ok","quote_status":"unverified","prev":"56281e5da405dc3b98aebe2b47e2344c9964132e11fee5959afd12127e33cead","hash":"dbdd26546be82eaea5363a9feac5de5f1bebc3b5dfcff5454a0d7207b60ca9c2"},{"id":"s5","type":"other","url":"https://en.wikipedia.org/wiki/Paul_Ehrenfest","title":"Paul Ehrenfest","quote":"","summary":"Biographical summary of scope of contributions.","claim_ids":["c5"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-08T06:50:18.655Z","link_status":"ok","quote_status":"na","prev":"dbdd26546be82eaea5363a9feac5de5f1bebc3b5dfcff5454a0d7207b60ca9c2","hash":"2bf147b7eb7c30d37952e5e8e98b41481b64042b36b2b5f01cef797c9a189720"},{"id":"s6","type":"other","url":"https://www.pnas.org/doi/10.1073/pnas.1421798112","title":"Ergodic theorem, ergodic theory, and statistical mechanics","quote":"This hypothesis states that some orbit of the flow will pass arbitrarily close to every point of phase space.","summary":"Clarifies limits of the quasi-ergodic hypothesis.","claim_ids":["c6"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-08T06:50:18.655Z","link_status":"http_403","quote_status":"unverified","prev":"2bf147b7eb7c30d37952e5e8e98b41481b64042b36b2b5f01cef797c9a189720","hash":"0e57741cdbaa2142faead6a07f37bef2109c3d67c415452bd81dd8d4607b16af"}]}