{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CVSZAPXMMNH5VYLFRDLKBGJZMQ","short_pith_number":"pith:CVSZAPXM","schema_version":"1.0","canonical_sha256":"1565903eec634fdae16588d6a09939641226ae345b1d8e9e19be60e3f36db9d0","source":{"kind":"arxiv","id":"1510.06219","version":2},"attestation_state":"computed","paper":{"title":"A generalization of Onsager's reciprocity relations to gradient flows with nonlinear mobility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.PR","physics.chem-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"A. Mielke, D. R. M. Renger, M. A. Peletier","submitted_at":"2015-10-21T11:48:15Z","abstract_excerpt":"Onsager's 1931 `reciprocity relations' result connects microscopic time-reversibility with a symmetry property of corresponding macroscopic evolution equations. Among the many consequences is a variational characterization of the macroscopic evolution equation as a gradient-flow, steepest-ascent, or maximal-entropy-production equation. Onsager's original theorem is limited to close-to-equilibrium situations, with a Gaussian invariant measure and a linear macroscopic evolution. In this paper we generalize this result beyond these limitations, and show how the microscopic time-reversibility lead"},"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":"1510.06219","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-10-21T11:48:15Z","cross_cats_sorted":["math.DS","math.PR","physics.chem-ph"],"title_canon_sha256":"bcd5bf56b45e883ba503d7e2fbc638d84aa5d0db0ddbe259f3431ed5e2d7a99a","abstract_canon_sha256":"c9c3e9fbc8737479512378ce9ee9c2ae2b22babe6b97a33f081a5539dbcec45d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:26.490808Z","signature_b64":"xWjgMottmy8Kor4uxORV9dnbBJUqK5dxlzf6iYpTOBvvIP1Q5fSXnIYyqn8YxMB2x7gNG/7zoYilPLWjdHMoDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1565903eec634fdae16588d6a09939641226ae345b1d8e9e19be60e3f36db9d0","last_reissued_at":"2026-05-18T00:03:26.490390Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:26.490390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A generalization of Onsager's reciprocity relations to gradient flows with nonlinear mobility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.PR","physics.chem-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"A. Mielke, D. R. M. Renger, M. A. Peletier","submitted_at":"2015-10-21T11:48:15Z","abstract_excerpt":"Onsager's 1931 `reciprocity relations' result connects microscopic time-reversibility with a symmetry property of corresponding macroscopic evolution equations. Among the many consequences is a variational characterization of the macroscopic evolution equation as a gradient-flow, steepest-ascent, or maximal-entropy-production equation. Onsager's original theorem is limited to close-to-equilibrium situations, with a Gaussian invariant measure and a linear macroscopic evolution. In this paper we generalize this result beyond these limitations, and show how the microscopic time-reversibility lead"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06219","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.06219","created_at":"2026-05-18T00:03:26.490457+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.06219v2","created_at":"2026-05-18T00:03:26.490457+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06219","created_at":"2026-05-18T00:03:26.490457+00:00"},{"alias_kind":"pith_short_12","alias_value":"CVSZAPXMMNH5","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"CVSZAPXMMNH5VYLF","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"CVSZAPXM","created_at":"2026-05-18T12:29:17.054201+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CVSZAPXMMNH5VYLFRDLKBGJZMQ","json":"https://pith.science/pith/CVSZAPXMMNH5VYLFRDLKBGJZMQ.json","graph_json":"https://pith.science/api/pith-number/CVSZAPXMMNH5VYLFRDLKBGJZMQ/graph.json","events_json":"https://pith.science/api/pith-number/CVSZAPXMMNH5VYLFRDLKBGJZMQ/events.json","paper":"https://pith.science/paper/CVSZAPXM"},"agent_actions":{"view_html":"https://pith.science/pith/CVSZAPXMMNH5VYLFRDLKBGJZMQ","download_json":"https://pith.science/pith/CVSZAPXMMNH5VYLFRDLKBGJZMQ.json","view_paper":"https://pith.science/paper/CVSZAPXM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.06219&json=true","fetch_graph":"https://pith.science/api/pith-number/CVSZAPXMMNH5VYLFRDLKBGJZMQ/graph.json","fetch_events":"https://pith.science/api/pith-number/CVSZAPXMMNH5VYLFRDLKBGJZMQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CVSZAPXMMNH5VYLFRDLKBGJZMQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CVSZAPXMMNH5VYLFRDLKBGJZMQ/action/storage_attestation","attest_author":"https://pith.science/pith/CVSZAPXMMNH5VYLFRDLKBGJZMQ/action/author_attestation","sign_citation":"https://pith.science/pith/CVSZAPXMMNH5VYLFRDLKBGJZMQ/action/citation_signature","submit_replication":"https://pith.science/pith/CVSZAPXMMNH5VYLFRDLKBGJZMQ/action/replication_record"}},"created_at":"2026-05-18T00:03:26.490457+00:00","updated_at":"2026-05-18T00:03:26.490457+00:00"}