{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"4f50f36961b6c9931d9694764d27f42823f6ad125cf28bb333d3141ff78f06a4","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"c4916602ad48132d6acce5eda2ddb0e67c5f2e10ddae966d6506ae3a201bd067","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":[],"external_id":"stat.fput-thermalization.toda-metastable-state","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"The FPUT chain is close to the Toda chain, a solvable model with as many conserved quantities as particles. The question is whether the long-lived non-thermal state of FPUT is the equilibrium of the Toda chain, and how fast its conserved quantities drift.","posed_since":"","precise":"Determine whether the pre-thermal state of the $\\alpha$-FPUT chain at small $\\epsilon$ is described by a generalized Gibbs ensemble built from Toda integrals, and find the scaling with $\\epsilon$ and $N$ of the drift time of these integrals, which sets $T_{\\mathrm{eq}}$. An answer is a mechanism with a scaling law consistent with simulations.","problem_ref":null,"references":"","settled_by":"Simulations tracking all Toda integrals in FPUT dynamics, with their drift rates derived from perturbation theory around Toda.","status_note":"Simulations using Toda integrals as slowly varying quantities support this picture (arXiv:2511.08149, 2025); reported scaling exponents differ between studies.","title":"Role of Toda integrals in the FPUT metastable state","topic_ref":"b026e7f128afdc43ebc73cc909210ea680a0ba040cd45dc5b34d5a420020f836"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"7cef9615788a850aca156c5971c2c0d90e14e4a5c0c7561a803f88c2a44a0eb4","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"04285873feb7053e44160877e20a0cdb82d362ac68fbb2bfa930721833b90e78","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"U9MNHClAUCn6BaeD5X7rCszNmGAz7gXa9xAidvkItA1Vcg-oyfzWD0KXEACtsSnbFwM9hu6eca5mLzt-YjDUBg"},"schema":"pubphys.envelope/1"},"record_hash":"7cef9615788a850aca156c5971c2c0d90e14e4a5c0c7561a803f88c2a44a0eb4","leaf_index":2081}