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

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.