{"paper":{"title":"Kinetic Path Summation, Multi--Sheeted Extension of Master Equation, and Evaluation of Ergodicity Coefficient","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"physics.comp-ph","authors_text":"A.N. Gorban","submitted_at":"2010-06-21T17:27:17Z","abstract_excerpt":"We study the Master equation with time--dependent coefficients, a linear kinetic equation for the Markov chains or for the monomolecular chemical kinetics. For the solution of this equation a path summation formula is proved. This formula represents the solution as a sum of solutions for simple kinetic schemes (kinetic paths), which are available in explicit analytical form. The relaxation rate is studied and a family of estimates for the relaxation time and the ergodicity coefficient is developed. To calculate the estimates we introduce the multi--sheeted extensions of the initial kinetics. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4128","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"}