{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MXA2CZAJ7F4EL2T554H3T3WU42","short_pith_number":"pith:MXA2CZAJ","canonical_record":{"source":{"id":"1607.01331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-07-05T17:12:52Z","cross_cats_sorted":[],"title_canon_sha256":"38911ee9f4aaf4826470c78767536fcaeb5dcc5e0779c19a013e753b9ca6f991","abstract_canon_sha256":"b6f280a2c99615482265b57f2c65543b220d80838e08a8be1622cc9b5862cc6e"},"schema_version":"1.0"},"canonical_sha256":"65c1a16409f97845ea7def0fb9eed4e6966fb6d4496e2d9fd00de62e48555b8d","source":{"kind":"arxiv","id":"1607.01331","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01331","created_at":"2026-05-18T01:11:29Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01331v1","created_at":"2026-05-18T01:11:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01331","created_at":"2026-05-18T01:11:29Z"},{"alias_kind":"pith_short_12","alias_value":"MXA2CZAJ7F4E","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MXA2CZAJ7F4EL2T5","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MXA2CZAJ","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MXA2CZAJ7F4EL2T554H3T3WU42","target":"record","payload":{"canonical_record":{"source":{"id":"1607.01331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-07-05T17:12:52Z","cross_cats_sorted":[],"title_canon_sha256":"38911ee9f4aaf4826470c78767536fcaeb5dcc5e0779c19a013e753b9ca6f991","abstract_canon_sha256":"b6f280a2c99615482265b57f2c65543b220d80838e08a8be1622cc9b5862cc6e"},"schema_version":"1.0"},"canonical_sha256":"65c1a16409f97845ea7def0fb9eed4e6966fb6d4496e2d9fd00de62e48555b8d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:29.815153Z","signature_b64":"DVcePRroyFfy7PzupjivhXZtXxNXXwNBf/vrPIRaNDg13g29jXW+rlRCxDBsDuQ99R5ftyW3ul6GKmY82Wg2Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65c1a16409f97845ea7def0fb9eed4e6966fb6d4496e2d9fd00de62e48555b8d","last_reissued_at":"2026-05-18T01:11:29.814628Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:29.814628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.01331","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d2EreG2VJJxSewcNTbBlFNI28y/fjSt29xGaRidyUCbfmNAYsybrBDZYwNoQ2vyhBF1TTpsVLAZUvoT6EjnvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:52:55.811218Z"},"content_sha256":"2f4e330815735eb642ad9e52800ac8c490d5137710d0e54d4cb2876e8ca8caf5","schema_version":"1.0","event_id":"sha256:2f4e330815735eb642ad9e52800ac8c490d5137710d0e54d4cb2876e8ca8caf5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MXA2CZAJ7F4EL2T554H3T3WU42","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Probability current and thermodynamics of open quantum systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alexander New, Benjamin Schumacher, Haifeng Qiao, Michael D. Westmoreland","submitted_at":"2016-07-05T17:12:52Z","abstract_excerpt":"This paper explores the generalization of the concept of a \"probability current\", familiar from wave-function quantum mechanics, to quantum systems with finite-dimensional Hilbert spaces. The generalized definition applies both to isolated systems evolving via the Schr\\\"odinger equation and to more general open systems obeying the Lindblad master equation. We establish several properties of the probability current and explore its relation to thermodynamic heat and work."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01331","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EUIex7hT18jBfsgs02GjrCiLwjtdEPHmldrSNqZowIfzU5+9TbKotZQVLYCZ6FIqQoYWlOUXqhD6uXf8ke1IDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:52:55.811787Z"},"content_sha256":"bdae1d939b410d4cf5b77024b11adf4a45db94bc614f8c69d3936ec23912f682","schema_version":"1.0","event_id":"sha256:bdae1d939b410d4cf5b77024b11adf4a45db94bc614f8c69d3936ec23912f682"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MXA2CZAJ7F4EL2T554H3T3WU42/bundle.json","state_url":"https://pith.science/pith/MXA2CZAJ7F4EL2T554H3T3WU42/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MXA2CZAJ7F4EL2T554H3T3WU42/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T03:52:55Z","links":{"resolver":"https://pith.science/pith/MXA2CZAJ7F4EL2T554H3T3WU42","bundle":"https://pith.science/pith/MXA2CZAJ7F4EL2T554H3T3WU42/bundle.json","state":"https://pith.science/pith/MXA2CZAJ7F4EL2T554H3T3WU42/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MXA2CZAJ7F4EL2T554H3T3WU42/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MXA2CZAJ7F4EL2T554H3T3WU42","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":"b6f280a2c99615482265b57f2c65543b220d80838e08a8be1622cc9b5862cc6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-07-05T17:12:52Z","title_canon_sha256":"38911ee9f4aaf4826470c78767536fcaeb5dcc5e0779c19a013e753b9ca6f991"},"schema_version":"1.0","source":{"id":"1607.01331","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01331","created_at":"2026-05-18T01:11:29Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01331v1","created_at":"2026-05-18T01:11:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01331","created_at":"2026-05-18T01:11:29Z"},{"alias_kind":"pith_short_12","alias_value":"MXA2CZAJ7F4E","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MXA2CZAJ7F4EL2T5","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MXA2CZAJ","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:bdae1d939b410d4cf5b77024b11adf4a45db94bc614f8c69d3936ec23912f682","target":"graph","created_at":"2026-05-18T01:11:29Z","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":"This paper explores the generalization of the concept of a \"probability current\", familiar from wave-function quantum mechanics, to quantum systems with finite-dimensional Hilbert spaces. The generalized definition applies both to isolated systems evolving via the Schr\\\"odinger equation and to more general open systems obeying the Lindblad master equation. We establish several properties of the probability current and explore its relation to thermodynamic heat and work.","authors_text":"Alexander New, Benjamin Schumacher, Haifeng Qiao, Michael D. Westmoreland","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-07-05T17:12:52Z","title":"Probability current and thermodynamics of open quantum systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01331","kind":"arxiv","version":1},"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":"sha256:2f4e330815735eb642ad9e52800ac8c490d5137710d0e54d4cb2876e8ca8caf5","target":"record","created_at":"2026-05-18T01:11:29Z","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":"b6f280a2c99615482265b57f2c65543b220d80838e08a8be1622cc9b5862cc6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-07-05T17:12:52Z","title_canon_sha256":"38911ee9f4aaf4826470c78767536fcaeb5dcc5e0779c19a013e753b9ca6f991"},"schema_version":"1.0","source":{"id":"1607.01331","kind":"arxiv","version":1}},"canonical_sha256":"65c1a16409f97845ea7def0fb9eed4e6966fb6d4496e2d9fd00de62e48555b8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65c1a16409f97845ea7def0fb9eed4e6966fb6d4496e2d9fd00de62e48555b8d","first_computed_at":"2026-05-18T01:11:29.814628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:29.814628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DVcePRroyFfy7PzupjivhXZtXxNXXwNBf/vrPIRaNDg13g29jXW+rlRCxDBsDuQ99R5ftyW3ul6GKmY82Wg2Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:29.815153Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.01331","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f4e330815735eb642ad9e52800ac8c490d5137710d0e54d4cb2876e8ca8caf5","sha256:bdae1d939b410d4cf5b77024b11adf4a45db94bc614f8c69d3936ec23912f682"],"state_sha256":"3a48c6186991c16aef3afc885e6b0446d756355144feccd1cfd54b7077110ff3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"picWQkQiY/lHdeF+b7+AjF/7KJZ39Mc2sNsPiMGTrcNA0mdd06jvcxA5M/5slV8idWOltEF2urP5aQZZo+oXAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:52:55.815594Z","bundle_sha256":"7160afee7da974654b2ef4d47a504da37780ca3a57d1a28989494fc776c40d6d"}}