Tackling master equations with a flux loop transform

TL;DR

This paper introduces a flux loop transform method to represent non-equilibrium system dynamics, restoring detailed balance and simplifying the steady state analysis with a new algorithm and free energy functional.

Contribution

It presents a novel flux loop transform that converts non-equilibrium dynamics into a form obeying detailed balance, enabling easier steady state analysis.

Findings

Restores detailed balance in non-equilibrium systems

Provides a new algorithm for steady state density construction

Defines a free energy functional minimized at steady state

Abstract

A procedure is introduced which allows to represent the dynamics of a non-equilibrium system violating detailed balance by its steady state loop fluxes. It is shown that detailed balance is restored in this representation, such that the non-equilibrium steady state follows a simple Boltzmann distribution. A novel algorithm for the construction of the steady state densities naturally emerges, as well as an expression for a 'free energy' functional which attains a minimum in the steady state.