{"paper":{"title":"Log-Sobolev inequalities for boundary-driven anharmonic chains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Jianfeng Lu","submitted_at":"2026-07-15T15:40:08Z","abstract_excerpt":"We study the non-equilibrium steady state of a weakly anharmonic chain of $N$ oscillators driven at its boundary by Langevin thermostats at unequal temperatures. Under a perturbative weak-anharmonicity condition, we prove a full-gradient logarithmic Sobolev inequality whose constant is independent of the chain length $N$. For homogeneous pinned chains, an additional quantitative regularity assumption yields a boundary space-time logarithmic Sobolev inequality and relative-entropy decay on the same $O(N^3)$ relaxation time scale as the harmonic chain. The proof extracts a finite-dimensional Gau"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13953","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.13953/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}