Thermodynamic uncertainty relation for first-passage times on Markov chains

TL;DR

This paper establishes a thermodynamic uncertainty relation for first-passage times in Markov chains, linking entropy production and flux to bound fluctuations, applicable across diverse out-of-equilibrium systems.

Contribution

It introduces a novel TUR for FPTs on Markov chains that accounts for bidirectional and unidirectional transitions, providing a versatile and optimized bound.

Findings

Provides a lower bound on FPT fluctuations using entropy production and flux.

Applicable to arbitrary initial conditions and out-of-equilibrium dynamics.

Enables analysis of diverse first-passage problems across disciplines.

Abstract

We derive a thermodynamic uncertainty relation (TUR) for first-passage times (FPTs) on continuous time Markov chains. The TUR utilizes the entropy production coming from bidirectional transitions, and the net flux coming from unidirectional transitions, to provide a lower bound on FPT fluctuations. As every bidirectional transition can also be seen as a pair of separate unidirectional ones, our approach typically yields an ensemble of TURs. The tightest bound on FPT fluctuations can then be obtained from this ensemble by a simple and physically motivated optimization procedure. The results presented herein are valid for arbitrary initial conditions, out-of-equilibrium dynamics, and are therefore well suited to describe the inherently irreversible first-passage event. They can thus be readily applied to a myriad of first-passage problems that arise across a wide range of disciplines.