{"paper":{"title":"Entropy Geometry and Normalized Means on Infinite-Dimensional Hamiltonian Manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Jean-Pierre Magnot","submitted_at":"2026-07-21T13:23:40Z","abstract_excerpt":"We propose a geometric--analytic framework for equilibrium statistical mechanics on infinite-dimensional Hamiltonian systems. In situations where no suitable $\\sigma$-additive invariant measure is available, we use \\emph{normalized means}, which generalize probability measures and normalized integrals. This construction yields entropy and free-energy functionals on weak symplectic Fr\\'echet manifolds and gives existence and uniqueness of exponential-family equilibrium states under explicit admissibility and separation assumptions. These states are stationary under Hamiltonian flows preserving "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28660","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/2607.28660/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}