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Kinetic path summation, multi-sheeted extension of master equation, and evaluation of ergodicity coefficient

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  • Gorban, A.N.

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.

Suggested Citation

  • Gorban, A.N., 2011. "Kinetic path summation, multi-sheeted extension of master equation, and evaluation of ergodicity coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(6), pages 1009-1025.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:6:p:1009-1025
    DOI: 10.1016/j.physa.2010.11.030
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