Entropy production related properties of first passage process

TL;DR

This paper investigates how entropy production influences key properties of first passage processes in stochastic thermodynamics, providing approximate formulas and uncertainty relations for mean first passage time and total jumps.

Contribution

It introduces approximated expressions for FPT and TNJ, and establishes uncertainty relations in the context of nonequilibrium birth-death processes.

Findings

Mean FPT decreases exponentially with entropy production.

Mean TNJ initially decreases exponentially then approaches a limit.

CVs of FPT and TNJ exhibit exponential decay or tend to one depending on bias.

Abstract

With nontrivial entropy production, first passage process is one of the most common nonequilibrium process in stochastic thermodynamics. Using one dimensional birth and death precess as a model framework, approximated expressions of mean first passage time (FPT), mean total number of jumps (TNJ), and their coefficients of variation (CV), are obtained for the case far from equilibrium. Consequently, uncertainty relations for FPT and TNJ are presented. Generally, mean FPT decreases exponentially with entropy production, while mean TNJ decreases exponentially first and then tends to a starting site dependent limit. For forward biased process, the CV of TNJ decreases exponentially with entropy production, while that of FPT decreases exponentially first and then tends to a starting site dependent limit. For backward biased process, both CVs of FPT and TNJ tend to one for large absolute values of entropy production. Related properties about the case of equilibrium are also addressed briefly for comparison.