{"paper":{"title":"Partially Thermostated Kac Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Hagop Tossounian, Ranjini Vaidyanathan","submitted_at":"2015-01-25T01:48:48Z","abstract_excerpt":"We study a system of $N$ particles interacting through the Kac collision, with $m$ of them interacting, in addition, with a Maxwellian thermostat at temperature $\\frac{1}{\\beta}$. We use two indicators to understand the approach to the equilibrium Gaussian state. We prove that i) the spectral gap of the evolution operator behaves as $\\frac{m}{N}$ for large $N$ ii) the relative entropy approaches its equilibrium value (at least) at an eventually exponential rate $\\sim \\frac{m}{N^2}$ for large $N$. The question of having non-zero entropy production at time $0$ remains open. A relationship betwee"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06104","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"}