Improved diffusive approximation of Markov jump processes close to equilibrium

Diffusive approximations of Markov jump processes, such as the Kramers-Moyal expansion, often fail to accurately capture the large, rare fluctuations that govern metastable systems. This is a critical problem for modeling phenomena like soft error rates in electronic memories, where these rare events are the object of interest. We introduce an improved diffusive approximation based on a modified diffusion tensor that replaces the standard arithmetic mean of forward and reverse jump rates with their logarithmic mean. This approach generalizes a method previously restricted to systems at detailed balance. Using new tools from stochastic thermodynamics, we prove the approximation's validity to linear order in departures from equilibrium. We numerically demonstrate that our method provides superior accuracy over the Kramers-Moyal expansion for predicting both steady-state distributions and transient properties, including the error rate of a bistable CMOS memory.