{"paper":{"title":"Symmetry, chaos and temperature in the one-dimensional lattice $\\phi^4$ theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"nlin.CD","authors_text":"Kenichiro Aoki","submitted_at":"2018-01-09T10:17:34Z","abstract_excerpt":"The symmetries of the minimal $\\phi^4$ theory on the lattice are systematically analyzed. We find that symmetry can restrict trajectories to subspaces, while their motions are still chaotic. The chaotic dynamics of autonomous Hamiltonian systems are discussed, in relation to the thermodynamic laws. Possibilities of configurations with non-equal ideal gas temperatures in the steady state, in Hamiltonian systems, are investigated, and examples of small systems in which the ideal gas temperatures are different within the system are found. The pairing of local (finite-time) Lyapunov exponents are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02865","kind":"arxiv","version":2},"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"}