{"paper":{"title":"An Elementary Proof of Lyapunov Exponent Pairing for Hard-Sphere Systems at Constant Kinetic Energy","license":"","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"nlin.CD","authors_text":"Debabrata Panja","submitted_at":"2001-07-21T08:43:26Z","abstract_excerpt":"The conjugate pairing of Lyapunov exponents for a field-driven system with smooth inter-particle interaction at constant total kinetic energy was first proved by Dettmann and Morriss [Phys. Rev. E {\\bf 53}, R5545 (1996)] using simple methods of geometry. Their proof was extended to systems interacting via hard-core inter-particle potentials by Wojtkowski and Liverani [Comm. Math. Phys. {\\bf 194}, 47 (1998)], using more sophisticated methods. Another, and somewhat more direct version of the proof for hard-sphere systems has been provided by Ruelle [J. Stat. Phys. {\\bf 95}, 393 (1999)]. However,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0107048","kind":"arxiv","version":4},"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"}