Stochastic description of electrochemical discharge using formalism of Kramers–Moyal expansion

Abstract

The formalism of Kramers–Moyal expansion is used for a stochastic description of one-stage electrochemical discharge occurring via a single route. In the stochastic model under consideration, an electrochemical reaction is represented as two independent random series of anodic and cathodic elementary acts of charge transfer. Each of two random series obeys its generalized Poisson’s distribution. Three Kramers–Moyal expansions are determined. The first Kramers–Moyal expansion works near the equilibrium potential. It takes into consideration both (anodic and cathodic) series of elementary acts. The second expansion determines the stochastic behavior of electrochemical reaction at high anodic potentials. The third expansion controls the stochastic behavior of electrochemical reaction in the range of high cathodic overpotentials. The dependence of coefficients of the Kramers–Moyal expansion on the macroscopic parameters of electrochemical discharge is determined. In view of interdisciplinary character of the theory of noise and fluctuations, a stochastic description of electrochemical discharge within the framework of Kramers–Moyal expansion is of interest also for the general theory of stochastic processes.