{"paper":{"title":"Phase Transitions in \"Small\" systems","license":"","headline":"","cross_cats":["nucl-th","physics.atm-clus"],"primary_cat":"cond-mat.stat-mech","authors_text":"D.H.E.Gross, E.Votyakov","submitted_at":"1999-11-17T14:13:20Z","abstract_excerpt":"Traditionally, phase transitions are defined in the thermodynamic limit only. We discuss how phase transitions of first order (with phase separation and surface tension), continuous transitions and (multi)-critical points can be seen and classified for small systems. Boltzmann defines the entropy as the logarithm of the area W(E,N)=e^S(E,N) of the surface in the mechanical N-body phase space at total energy E. The topology of the curvature determinant D(E,N) of S(E,N) allows the classification of phase transitions without taking the thermodynamic limit. The first calculation of the entire entr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9911257","kind":"arxiv","version":1},"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"}