{"paper":{"title":"Long memory constitutes a unified mesoscopic mechanism consistent with nonextensive statistical mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Ananias M. Mariz, Constantino Tsallis","submitted_at":"2011-06-15T20:50:51Z","abstract_excerpt":"We unify two paradigmatic mesoscopic mechanisms for the emergence of nonextensive statistics, namely the multiplicative noise mechanism leading to a {\\it linear} Fokker-Planck (FP) equation with {\\it inhomogenous} diffusion coefficient, and the non-Markovian process leading to the {\\it nonlinear} FP equation with {\\it homogeneous} diffusion coefficient. More precisely, we consider the equation $\\frac{\\partial p(x,t)}{\\partial t}=-\\frac{\\partial}{\\partial x}[F(x) p(x,t)] + 1/2D \\frac{\\partial^2}{\\partial x^2} [\\phi(x,p)p(x,t)]$, where $D \\in {\\cal R}$ and $F(x)=-\\partial V(x) /\\partial x$, $V(x"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3100","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"}