{"slug":"school-statistical-mechanics-boltzmann-formulation","verification":{"valid":true,"entries":3,"head":"e3f079e84ed6423a2bd3f32c415a13ebed0478d8698d7bb655a1e8fb84704e39"},"count":3,"sources":[{"id":"s1","type":"other","url":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","title":"Ludwig Boltzmann","quote":"In 1877, he provided the current definition of entropy, S = k_B ln Ω","summary":"Summarizes Boltzmann's 1877 entropy formula and key contributions.","claim_ids":["c1","c3"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-09T06:54:13.393Z","link_status":"ok","quote_status":"unverified","prev":"genesis","hash":"a0738196f004c54f707b069717575eb8957647afa0ee9263080b63566c15c5db"},{"id":"s2","type":"other","url":"https://en.wikipedia.org/wiki/H-theorem","title":"H-theorem","quote":"The H-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency of the quantity H to decrease","summary":"Documents the 1872 introduction and content of the H-theorem.","claim_ids":["c2"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-09T06:54:13.393Z","link_status":"ok","quote_status":"unverified","prev":"a0738196f004c54f707b069717575eb8957647afa0ee9263080b63566c15c5db","hash":"e604e70b68b0487c317020e8c78ab5f599bd853a6b317a17b09671c40226507c"},{"id":"s3","type":"other","url":"https://plato.stanford.edu/archives/fall2009/entries/statphys-Boltzmann/","title":"Boltzmann's Work in Statistical Physics","quote":"Zermelo presented another objection, now called the recurrence objection.","summary":"Details the recurrence and reversibility objections to Boltzmann's program.","claim_ids":["c4"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-09T06:54:13.393Z","link_status":"ok","quote_status":"verified","prev":"e604e70b68b0487c317020e8c78ab5f599bd853a6b317a17b09671c40226507c","hash":"e3f079e84ed6423a2bd3f32c415a13ebed0478d8698d7bb655a1e8fb84704e39"}]}