Non-equilibrium symmetry of cyclic first-passage times

TL;DR

This paper uncovers a symmetry in the distribution of cyclic first-passage times in stochastic systems, showing equilibrium and non-equilibrium cases differ by a fluctuation theorem and linking entropy production to trajectory symmetries.

Contribution

It introduces a new symmetry relation for cyclic first-passage times in non-equilibrium systems, connecting trajectory symmetry with entropy production.

Findings

At equilibrium, cyclic first-passage time distributions are identical clockwise and counterclockwise.

Out of equilibrium, these distributions are related by a detailed fluctuation theorem.

The symmetry relates entropy production along the cycle to the entire system's entropy production.

Abstract

We study the sum of first passage times along an arbitrary cycle made up of N>2 states of a small physical system. We show that, if the system is at thermodynamic equilibrium, this sum follows the same probability distribution regardless of whether the cycle is explored clockwise or counterclockwise. Out of equilibrium, the distributions of clockwise and counterclockwise cyclic first passage times are related by a detailed fluctuation theorem. This result descends from a symmetry of clockwise and counterclockwise trajectories, which combines time reversal with swapping portions of the trajectories. We then relate the entropy produced along the cycle with the entropy production of the whole system using large deviation theory. Our results reveal a novel symmetry in stochastic systems, of potential broad applicability in non-equilibrium physics.