{"paper":{"title":"Duration of local violations of the second law of thermodynamics along single trajectories in phase space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Daniel Dom\\'inguez, Reinaldo Garc\\'ia-Garc\\'ia","submitted_at":"2012-12-04T20:12:36Z","abstract_excerpt":"We define the {\\it violation fraction} $\\nu$ as the cumulative fraction of time that the entropy change is negative during single realizations of processes in phase space. This quantity depends both on the number of degrees of freedom $N$ and the duration of the time interval $\\tau$. In the large-$\\tau$ and large-$N$ limit we show that, for ergodic and microreversible systems, the mean value of $\\nu$ scales as $\\langle\\nu(N,\\tau)\\rangle\\sim\\big(\\tau N^{\\frac{1}{1+\\alpha}}\\big)^{-1}$. The exponent $\\alpha$ is positive and generally depends on the protocol for the external driving forces, being "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0844","kind":"arxiv","version":5},"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"}