{"paper":{"title":"Extremal property of a simple cycle","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"physics.chem-ph","authors_text":"A. N. Gorban","submitted_at":"2013-01-11T02:00:18Z","abstract_excerpt":"We study systems with finite number of states $A_i$ ($i=1,..., n$), which obey the first order kinetics (master equation) without detailed balance. For any nonzero complex eigenvalue $\\lambda$ we prove the inequality $\\frac{|\\Im \\lambda |}{|\\Re \\lambda |} \\leq \\cot\\frac{\\pi}{n}$. This bound is sharp and it becomes an equality for an eigenvalue of a simple irreversible cycle $A_1 \\to A_2 \\to... \\to A_n \\to A_1$ with equal rate constants of all transitions. Therefore, the simple cycle with the equal rate constants has the slowest decay of the oscillations among all first order kinetic systems wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2379","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"}