{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.topic/1","content_sha256":"4b74d10c3cc07f69f48d95292bc3f685750092e5dea81f231bbc9bc9124a44bc","created":"2026-10-03T07:17:52Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":[],"salt":"d23d9d00b752a3125e875d5000f13f0792b629de71ccd067be94e7979dfe7637","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"topic"},"content":{"external_id":"mathph.kinetic-limits","field":"mathph","n":"1","review_cite":"Y. Deng, Z. Hani, X. Ma, Hilbert's sixth problem: derivation of fluid equations via Boltzmann's kinetic theory, arXiv, 2025","review_link":"https://arxiv.org/abs/2503.01800","review_verified":"true","summary":"The Boltzmann equation describes a gas through the statistics of molecular collisions, and fluid equations follow from it; deriving both from Newton's laws for individual molecules is Hilbert's sixth problem. For a gas of hard spheres a derivation was posted in 2025 (Deng, Hani and Ma) and is under review, while other physically central cases remain unproven.","title":"Kinetic and fluid equations from particle dynamics","topic_ref":null,"why":"These derivations are the logical link between reversible microscopic mechanics and the irreversible macroscopic equations used across physics."},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"43f072b403d62b3c8ec7e10cd7a52d571053d785f7f84ce0ccb5bff0a60b87cc","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"de7e73e50df51066530b4b9a202343ed603e509c87cd5012089cfbabc17f5547","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"WiPcQUz6nb1oHS2tDVeCoCCnWELHvVagWliv163t4zI59O62Fap2ziPw5K-oYwSc3hVTAwoqewCa7bPkLgLSDA"},"schema":"pubphys.envelope/1"},"record_hash":"43f072b403d62b3c8ec7e10cd7a52d571053d785f7f84ce0ccb5bff0a60b87cc","leaf_index":262}