arXiv subjects

Yuta Sakamoto

Publications and source records attributed to Yuta Sakamoto.

3 recordsLinked to original sources

arXiv2025

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. 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.

cond-mat.stat-mech↗

arXiv2024

Method of Filtration in first passage time problems

Statistics of stochastic processes are crucially influenced by the boundary conditions. In one spatial dimension, for example, the first passage time distribution in semi-infinite space (one absorbing boundary) is markedly different from that in a finite interval with two absorbing boundaries. Here, we propose a method, which we refer to as a method of filtration, that allows us to construct the latter from only the knowledge of the former. We demonstrate that our method yields two solution forms, a method of eigenfunction expansion-like form and a method of image-like form. In particular, we argue that the latter solution form is a generalization of the method of image applicable to a stochastic process for which the method of image generally does not work, e.g., the Ornstein-Uhlenbeck process.

math-ph↗

arXiv2023

First passage time statistics of non-Markovian random walker: Onsager's regression hypothesis approach

First passage time plays a fundamental role in dynamical characterization of stochastic processes. Crucially, our current understanding on the problem is almost entirely relies on the theoretical formulations, which assume the processes under consideration are Markovian, despite abundant non-Markovian dynamics found in complex systems. Here we introduce a simple and physically appealing analytical framework to calculate the first passage time statistics of non-Markovian walkers grounded in a fundamental principle of nonequilibrium statistical physics that connects the fluctuations in stochastic system to the macroscopic law of relaxation. Pinpointing a crucial role of the memory in the first passage time statistics, our approach not only allows us to confirm the non-trivial scaling conjectures for fractional Brownian motion, but also provides a formula of the first passage time distribution in the entire time scale, and establish the quantitative description of the position probability distribution of non-Markovian walkers in the presence of absorbing boundary.

cond-mat.stat-mech↗