{"paper":{"title":"The Mesoscopic Partition Function:A Combined Spatial and Phase-Space Cell Structure","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Factorization of the mesoscopic partition function across spatial cells is equivalent to extensivity of the coarse-grained free energy.","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Bob Osano","submitted_at":"2026-05-01T12:52:42Z","abstract_excerpt":"We develop a mesoscopic formulation of equilibrium statistical mechanics based on coarse-grained occupation-number sectors of one-particle phase space. A mesoscopic partition function is constructed by averaging the microscopic Hamiltonian over configurations compatible with a given occupation profile. The construction converges to the canonical Gibbs partition function in the fine-graining limit and remains compatible with interacting many-body systems. Within this framework, thermodynamic extensivity is shown to be equivalent to asymptotic factorisation of the mesoscopic partition function, "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"factorisation of the mesoscopic partition function across spatial cells is equivalent to extensivity of the coarse-grained free energy, with deviations governed by inter-cell correlations quantifiable via mutual information","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The coarse-graining into combined spatial and phase-space cells is valid for classical many-body systems and the fine-graining limit exactly recovers the canonical partition function without further restrictions on particle interactions or cell boundaries.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A mesoscopic partition function equates factorization across spatial cells to extensivity of the coarse-grained free energy, with mutual-information corrections and a generalized Euler relation.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Factorization of the mesoscopic partition function across spatial cells is equivalent to extensivity of the coarse-grained free energy.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5c077c07152e8b46d882b27a1c4f27095661da94468018fba32931dbfeb3257f"},"source":{"id":"2605.00958","kind":"arxiv","version":2},"verdict":{"id":"0a258044-ed3a-4dc5-9293-a804c1b5f18c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T18:49:18.247406Z","strongest_claim":"factorisation of the mesoscopic partition function across spatial cells is equivalent to extensivity of the coarse-grained free energy, with deviations governed by inter-cell correlations quantifiable via mutual information","one_line_summary":"A mesoscopic partition function equates factorization across spatial cells to extensivity of the coarse-grained free energy, with mutual-information corrections and a generalized Euler relation.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The coarse-graining into combined spatial and phase-space cells is valid for classical many-body systems and the fine-graining limit exactly recovers the canonical partition function without further restrictions on particle interactions or cell boundaries.","pith_extraction_headline":"Factorization of the mesoscopic partition function across spatial cells is equivalent to extensivity of the coarse-grained free energy."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.00958/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T19:38:29.212047Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T17:57:58.579263Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"e99f812b405d8e261c94eab8c3ee33e5711603fa2d8710bf109c0f1d596ed65d"},"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"}