Violation of the method of images in non-Markovian processes and its connection to stochastic thermodynamics

Takuya Saito; Yuta Sakamoto; Takahiro Sakaue

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arXiv · 2512.01216

Violation of the method of images in non-Markovian processes and its connection to stochastic thermodynamics

Takuya Saito·Yuta Sakamoto·Takahiro Sakaue

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Abstract

We discuss a failure of the wide-spread method of images solution to describe the time evolution of probability distribution in diffusive processes with memory. For a path that touches a target during stochastic evolution, we define its conjugate twin of reflected path and show that their path probability ratio obeys a relation analogous to the fluctuation theorem. For systems reducible to the generalized Langevin equation with the fluctuation-dissipation relation, we suggest thermodynamic interpretation of the processes, which provides a quantitative basis as well as an intuitive physical picture on how and why the method of images breaks down for non-Markovian processes.

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Takuya Saito, Yuta Sakamoto, Takahiro Sakaue. 2025-12-01. Violation of the method of images in non-Markovian processes and its connection to stochastic thermodynamics. https://arxiv.org/abs/2512.01216

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