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  • Open Access

Thermodynamic uncertainty relation for first-passage times on Markov chains

Arnab Pal1,*, Shlomi Reuveni1,†, and Saar Rahav2,‡

  • 1School of Chemistry, Center for the Physics & Chemistry of Living Systems, Ratner Institute for Single Molecule Chemistry, and the Sackler Center for Computational Molecular & Materials Science, Tel Aviv University, 6997801 Tel Aviv, Israel
  • 2Schulich Faculty of Chemistry, Technion - Israel Institute of Technology, Haifa 3200008, Israel

  • *Corresponding author: arnabpal@mail.tau.ac.il
  • †shlomire@tauex.tau.ac.il
  • ‡rahavs@technion.ac.il
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Phys. Rev. Research 3, L032034 – Published 6 August, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L032034

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.

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Phys. Rev. Research 3, L032034– Published 6 August, 2021
  • Received 5 April 2021
  • Accepted 14 July 2021
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