Improved diffusive approximation of Markov jump processes close to equilibrium

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 recently developed 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 nonequilibrium electronic memory.