Improved diffusive approximation of Markov jump processes close to equilibrium

TL;DR

This paper introduces an improved diffusive approximation for Markov jump processes near equilibrium, enhancing accuracy in predicting large fluctuations and rare events, especially in non-equilibrium electronic memory systems.

Contribution

It extends previous methods to non-equilibrium systems using stochastic thermodynamics, providing a more accurate approximation for large fluctuations.

Findings

Better prediction of steady-state properties

More accurate transient behavior modeling

Reduced error rate in non-equilibrium electronic memory

Abstract

Diffusive approximations of Markov jump processes often fail to accurately capture large fluctuations. This is confounding, as the rare events triggered by these large fluctuations, such as the failure of electronic memories, are often the object of interest. In this paper we present an improved diffusive approximation, extending a method previously limited to equilibrium systems. Using new tools from stochastic thermodynamics, we prove its validity to linear order in departures from equilibrium and demonstrate its superior accuracy over the Kramers-Moyal expansion in predicting both steady-state and transient properties, including the error rate of a non-equilibrium electronic memory.