{"paper":{"title":"Fermi--Pasta--Ulam--Tsingou problems: Passage from Boltzmann to $q$-statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Constantino Tsallis, Debarshee Bagchi","submitted_at":"2017-09-25T21:28:28Z","abstract_excerpt":"The Fermi-Pasta-Ulam (FPU) one-dimensional Hamiltonian includes a quartic term which guarantees ergodicity of the system in the thermodynamic limit. Consistently, the Boltzmann factor $P(\\epsilon) \\sim e^{-\\beta \\epsilon}$ describes its equilibrium distribution of one-body energies, and its velocity distribution is Maxwellian, i.e., $P(v) \\sim e^{- \\beta v^2/2}$. We consider here a generalized system where the quartic coupling constant between sites decays as $1/d_{ij}^{\\alpha}$ $(\\alpha \\ge 0; d_{ij} = 1,2,\\dots)$. Through {\\it first-principle} molecular dynamics we demonstrate that, for larg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08729","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"}