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  • Open Access

Improved diffusive approximation of Markov jump processes close to equilibrium

David Roberts, Trevor McCourt*, Geremia Massarelli, Jeremy Rothschild, and Nahuel Freitas

  • Extropic Corporation, Cambridge, Massachusetts, USA

  • *Contact author: trevor@extropic.ai
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Phys. Rev. Research 8, 013161 – Published 11 February, 2026

DOI: https://doi.org/10.1103/dw4d-yj8c

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 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.

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Phys. Rev. Research 8, 013161– Published 11 February, 2026
  • Received 4 July 2025
  • Accepted 9 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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