Duality and fluctuation relations for statistics of currents on cyclic graphs

TL;DR

This paper establishes duality relations for current statistics in stochastic cyclic graphs and diffusion models, extending fluctuation relations beyond detailed balance and unifying previous no-pumping theorems.

Contribution

It introduces a general duality framework for current statistics in cyclic graphs and diffusion, valid beyond detailed balance, and connects existing fluctuation relations as special cases.

Findings

Derived exact relations for current statistics under dual protocols

Unified no-pumping theorems and fluctuation relations through duality

Extended fluctuation relations beyond detailed balance constraints

Abstract

We consider stochastic motion of a particle on a cyclic graph with arbitrarily periodic time dependent kinetic rates. We demonstrate duality relations for statistics of currents in this model and in its continuous version of a diffusion in one dimension. Our duality relations are valid beyond detailed balance constraints and lead to exact expressions that relate statistics of currents induced by dual driving protocols. We also show that previously known no-pumping theorems and some of the fluctuation relations, when they are applied to cyclic graphs or to one dimensional diffusion, are special consequences of our duality.