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It is known that statistical inequalities related to the weak bound can be obtained from the nonequilibrium work relation, $\\langle\\exp (-\\beta W)\\rangle = \\exp(-\\beta\\Delta F_T)$ . Here we derive an integral flu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1907.09604","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-07-22T22:08:00Z","cross_cats_sorted":[],"title_canon_sha256":"b9c3c9a03cea6ceed63974e16d6ce9b63c3c6598b917fccc61c90c669e8e3f9e","abstract_canon_sha256":"4744b89611117494725e7d6512021452189daf4e7b519f0a014e26ebc2ac6025"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:52.775156Z","signature_b64":"ZgJNbY0T1bxm4xhYl5hKf4INB4fIFLgWZa6vXnJsAa2DfpCxgTTnvlQYvI6SGJXkNBOC+eg+2qyOrIdU89rXDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd105b8572fa2911450b3e20e09c443ca62496433498fe12eb953c59944c63d9","last_reissued_at":"2026-05-17T23:39:52.774621Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:52.774621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fluctuation relations and strong inequalities for thermally isolated systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Christopher Jarzynski","submitted_at":"2019-07-22T22:08:00Z","abstract_excerpt":"For processes during which a macroscopic system exchanges no heat with its surroundings, the second law of thermodynamics places two lower bounds on the amount of work performed on the system: a weak bound, expressed in terms of a fixed-temperature free energy difference, $W \\ge \\Delta F_T$ , and a strong bound, given by a fixed-entropy internal energy difference, $W \\ge \\Delta E_S$ . It is known that statistical inequalities related to the weak bound can be obtained from the nonequilibrium work relation, $\\langle\\exp (-\\beta W)\\rangle = \\exp(-\\beta\\Delta F_T)$ . 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