{"paper":{"title":"Liouville's Theorem from the Principle of Maximum Caliber in Phase Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"Diego Gonz\\'alez, Sergio Davis","submitted_at":"2016-02-08T12:13:18Z","abstract_excerpt":"One of the cornerstones in non--equilibrium statistical mechanics (NESM) is Liouville's theorem, a differential equation for the phase space probability $\\rho(q,p; t)$. This is usually derived considering the flow in or out of a given surface for a physical system (composed of atoms), via more or less heuristic arguments.\n  In this work, we derive the Liouville equation as the partial differential equation governing the dynamics of the time-dependent probability $\\rho(q, p; t)$ of finding a \"particle\" with Lagrangian $L(q, \\dot{q}; t)$ in a specific point $(q, p)$ in phase space at time $t$, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03060","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"}