General technique of calculating drift velocity and diffusion coefficient in arbitrary periodic systems

TL;DR

This paper introduces a versatile method for calculating drift velocity and diffusion coefficients in periodic systems, applicable to both continuous and discrete-time models, with generalizations to higher dimensions.

Contribution

It provides a unified approach for computing drift and diffusion in arbitrary periodic systems, bridging continuous and discrete-time frameworks.

Findings

Both approaches yield the same drift velocity.

Diffusion coefficients differ by V*V/2 between approaches.

Method generalizes to higher-dimensional systems.

Abstract

We develop a practical method of computing the stationary drift velocity V and the diffusion coefficient D of a particle (or a few particles) in a periodic system with arbitrary transition rates. We solve this problem both in a physically relevant continuous-time approach as well as for models with discrete-time kinetics, which are often used in computer simulations. We show that both approaches yield the same value of the drift, but the difference between the diffusion coefficients obtained in each of them equals V*V/2. Generalization to spaces of arbitrary dimension and several applications of the method are also presented.