{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:L4MP24NJCACADISQ3VWKHEGUQ7","short_pith_number":"pith:L4MP24NJ","canonical_record":{"source":{"id":"1502.02122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-02-07T10:49:17Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"b3bf1553d4af91527505c94e5520dfafce5b0f14a7835b4d5682916872cf8643","abstract_canon_sha256":"adc796a2bbc1ea016b2b521356b69ac67b5920534c76dda42d26b1286d243be9"},"schema_version":"1.0"},"canonical_sha256":"5f18fd71a9100401a250dd6ca390d487cac9ce9a9a6d0c55ba2861d8b361963d","source":{"kind":"arxiv","id":"1502.02122","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02122","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02122v1","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02122","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"pith_short_12","alias_value":"L4MP24NJCACA","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"L4MP24NJCACADISQ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"L4MP24NJ","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:L4MP24NJCACADISQ3VWKHEGUQ7","target":"record","payload":{"canonical_record":{"source":{"id":"1502.02122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-02-07T10:49:17Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"b3bf1553d4af91527505c94e5520dfafce5b0f14a7835b4d5682916872cf8643","abstract_canon_sha256":"adc796a2bbc1ea016b2b521356b69ac67b5920534c76dda42d26b1286d243be9"},"schema_version":"1.0"},"canonical_sha256":"5f18fd71a9100401a250dd6ca390d487cac9ce9a9a6d0c55ba2861d8b361963d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:43.612522Z","signature_b64":"Wyy3E1dw+HnzlpVD4I1DAog3Tq8vCrFs/NNmy11Mlhruv0GJu2D/xxUOXF9lai0CcGE46kofUhvRVjYL7okRBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f18fd71a9100401a250dd6ca390d487cac9ce9a9a6d0c55ba2861d8b361963d","last_reissued_at":"2026-05-18T02:27:43.611905Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:43.611905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.02122","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":"2026-05-18T02:27:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TyXSNegFp04cfXLRgcG0TB0riIrq4bmhq4MxTbBt5KC0PTwIuekaA5Hhz6V5wkcMh6dpFvEqU5xcYOY2lKzwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:02:49.259588Z"},"content_sha256":"d10a62eeed5e7657e93d009b79cde521214a442d7b6da70e5a5147dae09ed4e3","schema_version":"1.0","event_id":"sha256:d10a62eeed5e7657e93d009b79cde521214a442d7b6da70e5a5147dae09ed4e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:L4MP24NJCACADISQ3VWKHEGUQ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lagrangian formulation of irreversible thermodynamics, and the second law of thermodynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"cond-mat.stat-mech","authors_text":"K. S. Glavatskiy","submitted_at":"2015-02-07T10:49:17Z","abstract_excerpt":"We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called \"mirror-image\" system. The Lagrangian is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the Lagrangian. Entropy increase in the normal system"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02122","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":"2026-05-18T02:27:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fGxx0nQny8U8RKjJWY2G+LSv473KCByToqWhrApwg8lQwNHD5Ya94ebQnzBSU5b6IWfjDPJ2RtrLMWxg36W/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:02:49.260191Z"},"content_sha256":"e92d59aeb4ab857c7cd69c9b77f6d7496a7f256de5460bd7ae4842b7ff1729c5","schema_version":"1.0","event_id":"sha256:e92d59aeb4ab857c7cd69c9b77f6d7496a7f256de5460bd7ae4842b7ff1729c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L4MP24NJCACADISQ3VWKHEGUQ7/bundle.json","state_url":"https://pith.science/pith/L4MP24NJCACADISQ3VWKHEGUQ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L4MP24NJCACADISQ3VWKHEGUQ7/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":"2026-06-11T23:02:49Z","links":{"resolver":"https://pith.science/pith/L4MP24NJCACADISQ3VWKHEGUQ7","bundle":"https://pith.science/pith/L4MP24NJCACADISQ3VWKHEGUQ7/bundle.json","state":"https://pith.science/pith/L4MP24NJCACADISQ3VWKHEGUQ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L4MP24NJCACADISQ3VWKHEGUQ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:L4MP24NJCACADISQ3VWKHEGUQ7","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":"adc796a2bbc1ea016b2b521356b69ac67b5920534c76dda42d26b1286d243be9","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-02-07T10:49:17Z","title_canon_sha256":"b3bf1553d4af91527505c94e5520dfafce5b0f14a7835b4d5682916872cf8643"},"schema_version":"1.0","source":{"id":"1502.02122","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02122","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02122v1","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02122","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"pith_short_12","alias_value":"L4MP24NJCACA","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"L4MP24NJCACADISQ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"L4MP24NJ","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:e92d59aeb4ab857c7cd69c9b77f6d7496a7f256de5460bd7ae4842b7ff1729c5","target":"graph","created_at":"2026-05-18T02:27:43Z","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":"We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called \"mirror-image\" system. The Lagrangian is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the Lagrangian. Entropy increase in the normal system","authors_text":"K. S. Glavatskiy","cross_cats":["cond-mat.soft"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-02-07T10:49:17Z","title":"Lagrangian formulation of irreversible thermodynamics, and the second law of thermodynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02122","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:d10a62eeed5e7657e93d009b79cde521214a442d7b6da70e5a5147dae09ed4e3","target":"record","created_at":"2026-05-18T02:27:43Z","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":"adc796a2bbc1ea016b2b521356b69ac67b5920534c76dda42d26b1286d243be9","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-02-07T10:49:17Z","title_canon_sha256":"b3bf1553d4af91527505c94e5520dfafce5b0f14a7835b4d5682916872cf8643"},"schema_version":"1.0","source":{"id":"1502.02122","kind":"arxiv","version":1}},"canonical_sha256":"5f18fd71a9100401a250dd6ca390d487cac9ce9a9a6d0c55ba2861d8b361963d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f18fd71a9100401a250dd6ca390d487cac9ce9a9a6d0c55ba2861d8b361963d","first_computed_at":"2026-05-18T02:27:43.611905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:43.611905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wyy3E1dw+HnzlpVD4I1DAog3Tq8vCrFs/NNmy11Mlhruv0GJu2D/xxUOXF9lai0CcGE46kofUhvRVjYL7okRBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:43.612522Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02122","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d10a62eeed5e7657e93d009b79cde521214a442d7b6da70e5a5147dae09ed4e3","sha256:e92d59aeb4ab857c7cd69c9b77f6d7496a7f256de5460bd7ae4842b7ff1729c5"],"state_sha256":"d8fb5bc3f073343d62da454a47bf6a75715bd8b1f4134185cda1ab6a4d641c49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zlzN3CaiUI5FSCL86lb33HOnoXqleOCyHfJ/EMGMDN88QF5MNtsj/zJL1ZOJW+S7Sa+T90VkxFUs7ZKrm3x3Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T23:02:49.263528Z","bundle_sha256":"c9ae093e10a25adfdea0e7c46437f0342fc41b978cb8e46a85fe7af2d5a3d862"}}