{"paper":{"title":"Perturbation Theory of the Free Energy via the Mesoscopic Combined Partition Function","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Bob Osano","submitted_at":"2026-05-18T09:28:19Z","abstract_excerpt":"We develop a systematic perturbation theory for the Helmholtz free energy of a classical $N$-body system within the mesoscopic framework of~\\cite{OsanoMeso,OsanoExtensivity}. The combined coarse-graining operator $\\mathcal{C}=\\mathcal{C}_x\\circ\\mathcal{C}_p$ acting on single-particle phase space partitions it into product cells $C_{i,\\alpha}=V_i\\times\\Pi_\\alpha$ and generates a mesoscopic partition function $\\mathcal{Z}_{\\rm meso}(\\lambda)$ whose reference level factorises by the multinomial theorem: $\\mathcal{Z}_{\\rm meso}^{(0)}=(Z_1^{(0)})^N$. Perturbation theory for $\\mathcal{F}_{\\rm meso}("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18121","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18121/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-19T23:41:59.144250Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.402342Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"f370b46c815b54c41098fee028fc81b00291f071bfbd1d251ed1017b4bc553ea"},"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"}