{"paper":{"title":"A variational formula for the free energy of an interacting many-particle system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Andrea Collevecchio, Stefan Adams, Wolfgang K\\\"onig","submitted_at":"2010-03-06T15:24:46Z","abstract_excerpt":"We consider $N$ bosons in a box in $\\mathbb {R}^d$ with volume $N/\\rho$ under the influence of a mutually repellent pair potential. The particle density $\\rho\\in (0,\\infty)$ is kept fixed. Our main result is the identification of the limiting free energy, $f(\\beta,\\rho)$, at positive temperature $1/\\beta$, in terms of an explicit variational formula, for any fixed $\\rho$ if $\\beta$ is sufficiently small, and for any fixed $\\beta$ if $\\rho$ is sufficiently small. The thermodynamic equilibrium is described by the symmetrized trace of $e^{-\\beta {\\mathcal{H}}_N}$, where ${\\mathcal{H}}_N$ denotes "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1393","kind":"arxiv","version":3},"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"}