{"slug":"school-ergodic-hypothesis-boltzmann-maxwell","verification":{"valid":true,"entries":5,"head":"fb05f4508e4509d410bded8fdc4a55526e48f9d4ff145381d2f31dc589c502f5"},"count":5,"sources":[{"id":"s1","type":"other","url":"https://link.springer.com/article/10.1007/BF00384333","title":"Boltzmann's ergodic hypothesis","quote":"Boltzmann's ergodic hypothesis is usually understood as the assumption that the trajectory of an isolated mechanical system runs through all states compatible with the total energy of the system.","summary":"Historical analysis of Boltzmann's formulation.","claim_ids":["c1"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-09T06:53:18.096Z","link_status":"ok","quote_status":"verified","prev":"genesis","hash":"6a4cca4d80b416268eb1ab06e9f3d0c1928f92fc510045845fd1c5441f51ddd5"},{"id":"s2","type":"other","url":"https://www.pnas.org/doi/10.1073/pnas.1421798112","title":"Ergodic theorem, ergodic theory, and statistical mechanics","quote":"The justification for this hypothesis is a problem that the originators of statistical mechanics, J. C. Maxwell and L. Boltzmann, confronted.","summary":"Discusses equality of averages.","claim_ids":["c2"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-09T06:53:18.096Z","link_status":"http_403","quote_status":"unverified","prev":"6a4cca4d80b416268eb1ab06e9f3d0c1928f92fc510045845fd1c5441f51ddd5","hash":"4da52f0ca8dc437b81e1972774f8d6d550a2e12215e733fd53508014f0b2ec3a"},{"id":"s3","type":"other","url":"https://plato.stanford.edu/archives/fall2011/entries/statphys-Boltzmann/","title":"Boltzmann's Work in Statistical Physics","quote":"Maxwell, J.C., (1879), 'On Boltzmann's theorem on the average distribution of energy in a system of material points'.","summary":"Lists Maxwell's 1879 paper.","claim_ids":["c3"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-09T06:53:18.096Z","link_status":"ok","quote_status":"unverified","prev":"4da52f0ca8dc437b81e1972774f8d6d550a2e12215e733fd53508014f0b2ec3a","hash":"0ad944db52b4741fabdca078ddeb58d7b7688bf5d5478a8f540eea493e8a7e12"},{"id":"s4","type":"other","url":"https://www.sciencedirect.com/topics/mathematics/ergodic-hypothesis","title":"Ergodic Hypothesis overview","quote":"In statistical physics, the Boltzmann–Maxwell ergodic hypothesis... prompted a search for ergodic mechanical systems.","summary":"Notes convergence to statistical patterns.","claim_ids":["c4"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-09T06:53:18.096Z","link_status":"http_403","quote_status":"unverified","prev":"0ad944db52b4741fabdca078ddeb58d7b7688bf5d5478a8f540eea493e8a7e12","hash":"8dca9f3162bfc6af78aa83ef9e1bfcf9ed0bd146bdb5b0eb561b4994d2d5db87"},{"id":"s5","type":"other","url":"https://link.springer.com/article/10.1007/BF00384333","title":"Boltzmann's ergodic hypothesis","quote":"The Ehrenfests critically reviewed Boltzmann's and Gibbs' approach... and identified three issues related to the ergodic hypothesis.","summary":"Details objections from Ehrenfests.","claim_ids":["c5"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-09T06:53:18.096Z","link_status":"ok","quote_status":"unverified","prev":"8dca9f3162bfc6af78aa83ef9e1bfcf9ed0bd146bdb5b0eb561b4994d2d5db87","hash":"fb05f4508e4509d410bded8fdc4a55526e48f9d4ff145381d2f31dc589c502f5"}]}