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arXiv · 2411.14004

Evaluation of the probability current in the stochastic path integral formalism

Valentin Wilhelm·Matthias Krüger·Matthias Fuchs·Florian Vogel
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Abstract

The probability current is a vital quantity in the Fokker-Planck description of stochastic processes. It characterizes non-equilibrium stationary states and appears in linear response calculations. We recover and review the probability current in the Onsager-Machlup functional approach to Markov processes by deriving a self-contained expression in general non-equilibrium fluctuation-dissipation relations using field theoretical methods. The derived formulas hold for non-constant drift and diffusion tensors and are explicitly evaluated in an Ornstein-Uhlenbeck process with non-reciprocal interactions specified as a harmonically bound particle in shear flow. Our work clarifies the concept of the probability current -- familiar from the Fokker-Planck equation -- in the path integral approach.

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Valentin Wilhelm, Matthias Krüger, Matthias Fuchs, Florian Vogel. 2024-11-21. Evaluation of the probability current in the stochastic path integral formalism. https://doi.org/10.1088/1751-8121%2Fadf534

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