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arXiv · 2507.03752

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

Adarsh Raghu·Izaak Neri
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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.

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Adarsh Raghu, Izaak Neri. 2025-07-04. Thermodynamic bounds and symmetries in first-passage problems of fluctuating currents. https://doi.org/10.1088/1367-2630/ae249e

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