Thermodynamic bounds and symmetries in first-passage problems of fluctuating currents

TL;DR

This paper introduces a method to derive thermodynamic bounds for first-passage problems in Markov chains, extending concepts like effective affinity and revealing symmetry properties of optimal fluctuating currents.

Contribution

It develops a novel approach combining coarse-graining and martingale methods to establish bounds and symmetries in first-passage problems for both discrete and continuous-time Markov chains.

Findings

Derived a thermodynamic bound on dissipation rate using splitting probability and first-passage time.

Extended the concept of effective affinity to discrete-time Markov chains.

Identified symmetry properties of optimal fluctuating currents.

Abstract

We develop a method for deriving thermodynamic bounds for first-passage problems of currents with two boundaries in Markov chains. Using this method, we derive a thermodynamic bound on the rate of dissipation in terms of the splitting probability and the first-passage time statistics of a fluctuating current, which is a refinement of a previously derived inequality. We also show that the concept of effective affinity, originally developed for continuous-time Markov chains, naturally extends to discrete-time Markov chains. Furthermore, we analyse symmetries in first-passage problems of fluctuating currents with two boundaries. We show that optimal currents -- those for which the effective affinity fully accounts for the dissipation -- satisfy a symmetry property: the current's average speed to reach the positive threshold equals the current's speed to reach the negative threshold. The developed approach uses a coarse-graining procedure for the average entropy production at random times and uses martingale methods to perform time-reversal of first-passage quantities.