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

Source: [Kinetic Path Summation, Multi--Sheeted Extension of Master Equation, and Evaluation of Ergodicity Coefficient](<https://www.sota2.com/research/paper/68fa29f91e209131ce839033>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T13:15:02.274Z

Authors: A.N. Gorban

Published: 2010-06-21T17:27:17.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1006.4128>)

[PDF](<https://arxiv.org/pdf/1006.4128.pdf>)