 Kinetic path summation, multi-sheeted extension of master equation, and evaluation of ergodicity coefficientA.N. Gorban Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 6, 1009-1025 Abstract: 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. This approach allows us to exploit the internal (“micro”) structure of the extended kinetics without perturbation of the base kinetics. Keywords: Path summation; Master equation; Ergodicity coefficient; Transition graph; Reaction network; Kinetics; Relaxation time; Replica (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:6:p:1009-1025 DOI: 10.1016/j.physa.2010.11.030 Access Statistics for this article Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis More articles in Physica A: Statistical Mechanics and its Applications from Elsevier |
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