Kinetic Path Summation, Multi--Sheeted Extension of Master Equation, and Evaluation of Ergodicity Coefficient

Details Kinetic Path Summation, Multi--Sheeted Extension of Master Equation, and Evaluation of Ergodicity Coefficient Kinetic Path Summation, Multi--Sheeted Extension of Master Equation, and Evaluation of Ergodicity Coefficient

2010-06-21

arxiv.org/abs/1006.4128v2

Physica A 390 (2011) 1009--1025

Physics

Computational Physics

The final journal version

Scientific paper

10.1016/j.physa.2010.11.030

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.

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