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

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. With a key quantity properly identified as the heat, the resultant thermodynamic interpretation of the processes 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.