{"paper":{"title":"Green-Kubo formula for weakly coupled system with dynamical noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Carlangelo Liverani, Cedric Bernardin, Francois Huveneers, Joel L. Lebowitz, Stefano Olla","submitted_at":"2013-11-28T17:38:09Z","abstract_excerpt":"We study the Green-Kubo (GK) formula $\\kappa (\\varepsilon, \\xi)$ for the heat conductivity of an infinite chain of $d$-dimensional finite systems (cells) coupled by a smooth nearest neighbour potential $\\varepsilon V$. The uncoupled systems evolve according to Hamiltonian dynamics perturbed stochastically by an energy conserving noise of strength $\\xi$. Noting that $\\kappa (\\varepsilon, \\xi)$ exists and is finite whenever $\\xi> 0$, we are interested in what happens when the strength of the noise $\\xi \\to 0$. For this, we start in this work by formally expanding $\\kappa (\\varepsilon, \\xi)$ in a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7384","kind":"arxiv","version":2},"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"}