Fluctuation relation in continuous-time random walks driven by an external field

TL;DR

This paper investigates a fluctuation relation in continuous-time random walks driven by an external field, showing its validity under certain conditions and analyzing the effects of boundaries and field exchange.

Contribution

It demonstrates the fluctuation relation's validity for noninteracting charge carriers with general waiting-time distributions and explores boundary effects and field exchange relevance.

Findings

Fluctuation relation holds regardless of lattice structure or waiting-time distribution.

The relation is valid after taking the continuum limit with reflecting boundaries.

Exchanging initial and final positions is equivalent to exchanging the field in free space.

Abstract

We study a fluctuation relation representing a nonequilibrium equality indicating that the ratio between the distribution of trajectories obtained by exchanging the initial and final positions is characterized by free energy differences for the duration of the trajectories. We examine the fluctuation relation for noninteracting charge carriers driven by an external electric field by using a continuous-time lattice random walk model with a general waiting-time distribution of transitions. The fluctuation relation is obtained regardless of the lattice structure factor or the form of the waiting-time distribution. However, the fluctuation relation is satisfied only after taking the continuum limit in the presence of a reflecting boundary. Moreover, in free space without boundary conditions, exchanging the initial and final positions is equivalent to exchanging the field (or drift) directions. However, we show that the exchanging field (or drift) directions is not relevant for studying the fluctuation relation under the reflecting boundary condition.