{"paper":{"title":"Variational Boundary Fluctuations as a First-Principles Origin of Langevin Noise","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Fluctuating endpoints in Hamilton's principle generate an effective Langevin force whose amplitude is filtered by the Hessian of the principal function.","cross_cats":["physics.class-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Francisco Monroy","submitted_at":"2026-05-17T19:35:17Z","abstract_excerpt":"Stochastic forces are usually postulated or obtained by eliminating environmental degrees of freedom. Here we identify a variational origin: fluctuating endpoint data in Hamilton's principle induce fluctuations of the on-shell action. Hamilton--Jacobi propagation transports this boundary imprint, whose gradient generates an effective Langevin force inherited from boundary-action fluctuations. The resulting force is not freely specifiable: its amplitude is filtered by the Hessian of Hamilton's principal function, yielding multiplicative and state-dependent noise. Homogeneous additive Langevin f"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"fluctuating endpoint data in Hamilton's principle induce fluctuations of the on-shell action. Hamilton--Jacobi propagation transports this boundary imprint, whose gradient generates an effective Langevin force inherited from boundary-action fluctuations. The resulting force is not freely specifiable: its amplitude is filtered by the Hessian of Hamilton's principal function, yielding multiplicative and state-dependent noise.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that boundary fluctuations can be treated as independent variational data whose imprint survives Hamilton-Jacobi propagation without being washed out by the deterministic dynamics or requiring additional regularization; this enters when the paper states that the gradient of the fluctuating on-shell action directly supplies the Langevin force (abstract and implied § derivation).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Fluctuating boundary data in Hamilton's principle propagate via Hamilton-Jacobi to produce state-dependent multiplicative Langevin forces, with additive noise recovered only after Markovian coarse-graining.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Fluctuating endpoints in Hamilton's principle generate an effective Langevin force whose amplitude is filtered by the Hessian of the principal function.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d0d87a091016c81c498eeeca17d94c2bf8a4ce0fe9db0ac6de9b5d4f66b1f67e"},"source":{"id":"2605.17621","kind":"arxiv","version":1},"verdict":{"id":"b8764fc6-8090-4a49-813a-4c8471343bd2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:24:41.042798Z","strongest_claim":"fluctuating endpoint data in Hamilton's principle induce fluctuations of the on-shell action. Hamilton--Jacobi propagation transports this boundary imprint, whose gradient generates an effective Langevin force inherited from boundary-action fluctuations. The resulting force is not freely specifiable: its amplitude is filtered by the Hessian of Hamilton's principal function, yielding multiplicative and state-dependent noise.","one_line_summary":"Fluctuating boundary data in Hamilton's principle propagate via Hamilton-Jacobi to produce state-dependent multiplicative Langevin forces, with additive noise recovered only after Markovian coarse-graining.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that boundary fluctuations can be treated as independent variational data whose imprint survives Hamilton-Jacobi propagation without being washed out by the deterministic dynamics or requiring additional regularization; this enters when the paper states that the gradient of the fluctuating on-shell action directly supplies the Langevin force (abstract and implied § derivation).","pith_extraction_headline":"Fluctuating endpoints in Hamilton's principle generate an effective Langevin force whose amplitude is filtered by the Hessian of the principal function."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17621/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"cited_work_retraction","ran_at":"2026-05-19T22:52:44.911177Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T22:31:19.520688Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:31:02.333203Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.565219Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:21:57.490987Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"05c2dc2c4bb83b31bf8a4465d4890ae0d196a68d23feac8fe7ba6e6b54a2443d"},"references":{"count":21,"sample":[{"doi":"","year":1976,"title":"L. 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