{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7WJS3A3XJZXX7JRMM4AD3GOMTL","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":"7d3a07548f2289508d5b15a50a8941defb7cea978166b3612823bd46ffc66a00","cross_cats_sorted":["cond-mat.mtrl-sci"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-11-20T21:15:48Z","title_canon_sha256":"251d0e1e9ecbf068332b705c1a56058794d7692434f83191ec29dab3b1fdc3cc"},"schema_version":"1.0","source":{"id":"1811.08492","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.08492","created_at":"2026-05-17T23:55:10Z"},{"alias_kind":"arxiv_version","alias_value":"1811.08492v1","created_at":"2026-05-17T23:55:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08492","created_at":"2026-05-17T23:55:10Z"},{"alias_kind":"pith_short_12","alias_value":"7WJS3A3XJZXX","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7WJS3A3XJZXX7JRM","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7WJS3A3X","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:e3fc6bb0ae002ea60003501d930fd7f4e31dbdd98028f2029b131a9c0694bf5c","target":"graph","created_at":"2026-05-17T23:55:10Z","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 propose a Fokker-Planck equation (FPE) theory to describe stochastic fluctuation and relaxation processes of lattice vibration at a wide range of conditions, including those beyond the phonon gas (PG) limit. Using the time-dependent, multiple state-variable probability function of a FPE, we first derive time-correlation functions of lattice heat currents in terms of correlation functions among multiple vibrational modes, and subsequently predict the thermal conductivity based on the Green-Kubo formalism. When the kinetic transport theories are valid, this FPE not only predicts a thermal con","authors_text":"Jianjun Dong, Yi Zeng","cross_cats":["cond-mat.mtrl-sci"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-11-20T21:15:48Z","title":"The Fokker-Planck Equation for Lattice Vibration: Stochastic Dynamics and Thermal Conductivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08492","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":"sha256:7d6384a509ab5878605474b770e37aed235ff96551f1b03554884fa9dbdb24ae","target":"record","created_at":"2026-05-17T23:55:10Z","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":"7d3a07548f2289508d5b15a50a8941defb7cea978166b3612823bd46ffc66a00","cross_cats_sorted":["cond-mat.mtrl-sci"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-11-20T21:15:48Z","title_canon_sha256":"251d0e1e9ecbf068332b705c1a56058794d7692434f83191ec29dab3b1fdc3cc"},"schema_version":"1.0","source":{"id":"1811.08492","kind":"arxiv","version":1}},"canonical_sha256":"fd932d83774e6f7fa62c67003d99cc9adc4dcda6870dd0de5fd5e4b4ba828aad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd932d83774e6f7fa62c67003d99cc9adc4dcda6870dd0de5fd5e4b4ba828aad","first_computed_at":"2026-05-17T23:55:10.983986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:10.983986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XXNSeBP8Lc3vTvpjq4QILwJmcVRPefg2XKBoGAZVCqwbHZwrdVtPGV4I7K0u1L/5aiP5LxOvR/KTaasBDCNrAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:10.984350Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.08492","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d6384a509ab5878605474b770e37aed235ff96551f1b03554884fa9dbdb24ae","sha256:e3fc6bb0ae002ea60003501d930fd7f4e31dbdd98028f2029b131a9c0694bf5c"],"state_sha256":"a63724d947d275f583b1c4aa9475db56b09074d33ff7541404e293ea9e4c7a9a"}