{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QICOMJBMBFN22CYZ32ELCUSPYI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d3087a4926b98b1b9a287928cca6ba46aed5941bf5993beb970f697fb87e5f8a","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-14T22:46:17Z","title_canon_sha256":"8b8a21388fe967c5f626627caec1c3e2c5e2da35fc78519b5b279063209fbb33"},"schema_version":"1.0","source":{"id":"1202.3169","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3169","created_at":"2026-05-18T03:58:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3169v2","created_at":"2026-05-18T03:58:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3169","created_at":"2026-05-18T03:58:24Z"},{"alias_kind":"pith_short_12","alias_value":"QICOMJBMBFN2","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QICOMJBMBFN22CYZ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QICOMJBM","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:21a8f423f502546b42ae51c2369a33be6c855bd12d660177b5636bef64117215","target":"graph","created_at":"2026-05-18T03:58:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In Physica A vol 387(24) (2008) pp6079-6094 [1], a kinetic equation for gas flows was proposed that leads to a set of four macroscopic conservation equations, rather than the traditional set of three equations. The additional equation arises due to local spatial random molecular behavior, which has been described as a volume or mass diffusion process. In this present paper, we describe a procedure to construct a Gibbs-type equation and a second-law associated with these kinetic and continuum models. We also point out the close link between the kinetic equation in [1] and that proposed previous","authors_text":"Jason M. Reese, S. Kokou Dadzie","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-14T22:46:17Z","title":"On the thermodynamics of volume/mass diffusion in fluids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3169","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8254da498cdb81ea57ca55e520df2ad5bec9e40da137b5538a498ffc5a708827","target":"record","created_at":"2026-05-18T03:58:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d3087a4926b98b1b9a287928cca6ba46aed5941bf5993beb970f697fb87e5f8a","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-14T22:46:17Z","title_canon_sha256":"8b8a21388fe967c5f626627caec1c3e2c5e2da35fc78519b5b279063209fbb33"},"schema_version":"1.0","source":{"id":"1202.3169","kind":"arxiv","version":2}},"canonical_sha256":"8204e6242c095bad0b19de88b1524fc2109aa17e62764579243cb7c0270c0406","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8204e6242c095bad0b19de88b1524fc2109aa17e62764579243cb7c0270c0406","first_computed_at":"2026-05-18T03:58:24.270114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:24.270114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QH1ha1wVRXw+GkiK22FNaxed2EgB2PJ4L6hT9vt/zfqD8YvDsg3nPi45wJRLVa2r70agBleDO3o+OTGxfiEhDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:24.270854Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3169","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8254da498cdb81ea57ca55e520df2ad5bec9e40da137b5538a498ffc5a708827","sha256:21a8f423f502546b42ae51c2369a33be6c855bd12d660177b5636bef64117215"],"state_sha256":"19d52ed9cdffb841d414bd664a92d63168ea1421ae44a4a72511678ceb8c8e19"}