Thermodynamic uncertainty relation for first-passage times on Markov chains

Arnab Pal*, Shlomi Reuveni, Saar Rahav

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article numberL032034
Number of pages6
JournalPhysical Review Research
Issue number3
StatePublished - Aug 2021


Dive into the research topics of 'Thermodynamic uncertainty relation for first-passage times on Markov chains'. Together they form a unique fingerprint.

Cite this