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Universal tradeoff relation between speed, uncertainty, and dissipation in nonequilibrium stationary states

by Izaak Neri

This Submission thread is now published as SciPost Phys. 12, 139 (2022)

Submission summary

As Contributors: Izaak Neri
Preprint link: scipost_202103_00027v3
Date accepted: 2022-04-12
Date submitted: 2022-02-09 21:23
Submitted by: Neri, Izaak
Submitted to: SciPost Physics
Academic field: Physics
  • Statistical and Soft Matter Physics
Approach: Theoretical


We derive universal thermodynamic inequalities that bound from below the moments of first-passage times of stochastic currents in nonequilibrium stationary states of Markov jump processes in the limit where the thresholds that define the first-passage problem are large. These inequalities describe a tradeoff between speed, uncertainty, and dissipation in nonequilibrium processes, which are quantified, respectively, with the moments of the first-passage times of stochastic currents, the splitting probability, and the mean entropy production rate. Near equilibrium, the inequalities imply that mean-first passage times are lower bounded by the Van't Hoff-Arrhenius law, whereas far from thermal equilibrium the bounds describe a universal speed limit for rate processes. When the current is the stochastic entropy production, then the bounds are equalities, a remarkable property that follows from the fact that the exponentiated negative entropy production is a martingale.

Published as SciPost Phys. 12, 139 (2022)

Author comments upon resubmission

The minor comments of the Referees have been implement, and some steps in the derivations have been further simplified and made more clear. In my opinion, the manuscript is now ready for publication.

List of changes

The following changes have been implemented:

*) some steps in the derivation of (3) that are based on large deviation theory have been simplified, which leads to a better understanding of (3). In particular, it is shown that (3) follows directly from (19), and there is no need to study the first-passage times at the negative boundary.

*) the derivation of formula (49) has been detailed in Appendix E

Reports on this Submission

Anonymous Report 1 on 2022-2-22 (Invited Report)


I have no objections to the answers given by the author and the changes made in the manuscript. I therefore agree that it should now be ready for acceptance.

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