{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"d7abd2be14d909d08dfcdd2fc983c52f6d085c327afd92a5dd8df65d242abfac","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"3735fba69deec6106fc8690f902210ad15f2f7a521c2c48b00719224dc21ccea","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"stat.nonequilibrium-steady-states.heat-conduction-exponent","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"In one-dimensional chains that conserve momentum, heat conductivity grows with chain length instead of staying fixed. Theory predicts universal growth exponents, but simulations of different chains disagree.","posed_since":"1997","precise":"For 1D anharmonic chains conserving energy, momentum and stretch (e.g., FPUT with asymmetric or symmetric potentials), determine the exponent delta in the conductivity $\\kappa(L) \\sim L^\\delta$. Nonlinear fluctuating hydrodynamics predicts $\\delta = 1/3$ for generic asymmetric potentials (FPUT-alpha-beta: KPZ sound modes and a Levy 5/3 heat mode); for the symmetric FPUT-beta chain numerics and mode-coupling theory support $\\delta = 2/5$. An answer is the exponent for each class, confirmed at sizes where finite-size drift is controlled.","problem_ref":null,"references":"","settled_by":"Nonequilibrium and equilibrium simulations at sizes where effective exponents stop drifting, agreeing with the hydrodynamic prediction for each class.","status_note":"Simulated exponents range roughly from 0.25 to 0.4 depending on model and size; a 2026 review attributes much of the spread to thermostat-induced finite-size effects (Lepri, Livi, Politi, arXiv:2602.15512).","title":"Universal exponent of anomalous heat conduction in one dimension","topic_ref":"72aaad1f1435578edfef33967b7b92010d17bf95ece739d074630e4e3fd7a09f"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"2fcac248fae95eaf4d78fb7589d24a106fde51f561cb5faab4a0b661e04a95c1","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"83308aa70d3cb514d55abcf212e92d55468e16d65f084d04e2db2c22ceb7586f","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"93eg2XL4w4nbhrgdfSz5LLDvWSsOghdBQFktyg9LtdKDCV5TLw_p1aUHDtB2vdavyxPWzYq81WxJfASYMLbUBw"},"schema":"pubphys.envelope/1"},"record_hash":"2fcac248fae95eaf4d78fb7589d24a106fde51f561cb5faab4a0b661e04a95c1","leaf_index":2106}