{"paper":{"title":"Hyperstatistical thermodynamics of the one-dimensional Klein-Gordon and Dirac oscillators: a closed-form q-generalized Boltzmann factor and a quantitative comparison with Beck's superstatistics","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Abdelmalek Boumali","submitted_at":"2026-06-05T15:54:15Z","abstract_excerpt":"We revisit the thermodynamics of the one-dimensional Klein-Gordon (KGO) and Dirac (DO) oscillators within two frameworks of generalized statistics: Beck's asymptotic superstatistics and the recently introduced hyperstatistics. In hyperstatistics, a $\\gamma$-distribution of domain Boltzmann factors yields, after Laplace transformation and averaging over a normalisable density $f(\\beta)$, the closed-form q-generalized Boltzmann factor $B_q(\\varepsilon) = \\exp_q(-\\langle\\beta\\rangle\\varepsilon)$, independent of $f(\\beta)$. We compute the partition function, entropy $S$, and specific heat $C_v$ fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12454","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/2606.12454/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"}