Time arrow in open-boundary one-dimensional stochastic dynamics

TL;DR

This paper investigates the irreversibility in a one-dimensional open-boundary Brownian system with a temperature gradient, revealing asymmetries in transition probabilities despite zero net probability current.

Contribution

It introduces a virtual-gyration framework to explain observed irreversibility in systems without net probability flow, combining simulation and theoretical analysis.

Findings

Asymmetry in transition probabilities indicates irreversibility.

Irreversibility peaks near the temperature interface.

Absence of probability current despite nonequilibrium conditions.

Abstract

We consider the finite-timestep Brownian dynamics of a single particle confined in one dimension, with a nonuniform temperature profile. In such an open-boundary scenario, one cannot observe any net probability current in the nonequilibrium steady state (NESS). On the other hand, the nonequilibrium nature of this system is exhibited through the asymmetry in forward and backward transition probabilities, as is reported in this work through the stochastic simulation analysis and theoretical arguments. The irreversibility becomes prominent nearby the temperature interface. We propose that the observed irreversibility can be accounted for via a virtual-gyration scenario, while the collapse of virtual gyrations upon the one-dimensional coordinate leads to the absence of probability current.