{"paper":{"title":"The Vlasov continuum limit for the classical microcanonical ensemble","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Michael K.-H. Kiessling","submitted_at":"2009-02-13T23:46:36Z","abstract_excerpt":"For classical Hamiltonian N-body systems with mildly regular pair interaction potential it is shown that when N tends to infinity in a fixed bounded domain, with energy E scaling quadratically in N proportional to e, then Boltzmann's ergodic ensemble entropy S(N,E) has the asymptotic expansion S(N,E) = - N log N + s(e) N + o(N); here, the N log N term is combinatorial in origin and independent of the rescaled Hamiltonian while s(e) is the system-specific Boltzmann entropy per particle, i.e. -s(e) is the minimum of Boltzmann's H-function for a perfect gas of \"energy\" e subjected to a combinatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2413","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}