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

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.