{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7WJS3A3XJZXX7JRMM4AD3GOMTL","short_pith_number":"pith:7WJS3A3X","schema_version":"1.0","canonical_sha256":"fd932d83774e6f7fa62c67003d99cc9adc4dcda6870dd0de5fd5e4b4ba828aad","source":{"kind":"arxiv","id":"1811.08492","version":1},"attestation_state":"computed","paper":{"title":"The Fokker-Planck Equation for Lattice Vibration: Stochastic Dynamics and Thermal Conductivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"cond-mat.stat-mech","authors_text":"Jianjun Dong, Yi Zeng","submitted_at":"2018-11-20T21:15:48Z","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"},"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":"1811.08492","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-11-20T21:15:48Z","cross_cats_sorted":["cond-mat.mtrl-sci"],"title_canon_sha256":"251d0e1e9ecbf068332b705c1a56058794d7692434f83191ec29dab3b1fdc3cc","abstract_canon_sha256":"7d3a07548f2289508d5b15a50a8941defb7cea978166b3612823bd46ffc66a00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:10.984350Z","signature_b64":"XXNSeBP8Lc3vTvpjq4QILwJmcVRPefg2XKBoGAZVCqwbHZwrdVtPGV4I7K0u1L/5aiP5LxOvR/KTaasBDCNrAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd932d83774e6f7fa62c67003d99cc9adc4dcda6870dd0de5fd5e4b4ba828aad","last_reissued_at":"2026-05-17T23:55:10.983986Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:10.983986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Fokker-Planck Equation for Lattice Vibration: Stochastic Dynamics and Thermal Conductivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"cond-mat.stat-mech","authors_text":"Jianjun Dong, Yi Zeng","submitted_at":"2018-11-20T21:15:48Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08492","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.08492","created_at":"2026-05-17T23:55:10.984042+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.08492v1","created_at":"2026-05-17T23:55:10.984042+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08492","created_at":"2026-05-17T23:55:10.984042+00:00"},{"alias_kind":"pith_short_12","alias_value":"7WJS3A3XJZXX","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"7WJS3A3XJZXX7JRM","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"7WJS3A3X","created_at":"2026-05-18T12:32:11.075285+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/7WJS3A3XJZXX7JRMM4AD3GOMTL","json":"https://pith.science/pith/7WJS3A3XJZXX7JRMM4AD3GOMTL.json","graph_json":"https://pith.science/api/pith-number/7WJS3A3XJZXX7JRMM4AD3GOMTL/graph.json","events_json":"https://pith.science/api/pith-number/7WJS3A3XJZXX7JRMM4AD3GOMTL/events.json","paper":"https://pith.science/paper/7WJS3A3X"},"agent_actions":{"view_html":"https://pith.science/pith/7WJS3A3XJZXX7JRMM4AD3GOMTL","download_json":"https://pith.science/pith/7WJS3A3XJZXX7JRMM4AD3GOMTL.json","view_paper":"https://pith.science/paper/7WJS3A3X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.08492&json=true","fetch_graph":"https://pith.science/api/pith-number/7WJS3A3XJZXX7JRMM4AD3GOMTL/graph.json","fetch_events":"https://pith.science/api/pith-number/7WJS3A3XJZXX7JRMM4AD3GOMTL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7WJS3A3XJZXX7JRMM4AD3GOMTL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7WJS3A3XJZXX7JRMM4AD3GOMTL/action/storage_attestation","attest_author":"https://pith.science/pith/7WJS3A3XJZXX7JRMM4AD3GOMTL/action/author_attestation","sign_citation":"https://pith.science/pith/7WJS3A3XJZXX7JRMM4AD3GOMTL/action/citation_signature","submit_replication":"https://pith.science/pith/7WJS3A3XJZXX7JRMM4AD3GOMTL/action/replication_record"}},"created_at":"2026-05-17T23:55:10.984042+00:00","updated_at":"2026-05-17T23:55:10.984042+00:00"}