Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation

Abstract

The infimum of an integrated current is its extreme value against the direction of its average flow. Using martingale theory, we show that the infima of integrated edge currents in time-homogeneous Markov jump processes are geometrically distributed, with a mean value determined by the effective affinity measured by a marginal observer that only sees the integrated edge current. In addition, we show that a marginal observer can estimate a finite fraction of the average entropy production rate in the underlying nonequilibrium process from the extreme value statistics in the integrated edge current. The estimated average rate of dissipation obtained in this way equals the above mentioned effective affinity times the average edge current. Moreover, we show that estimates of dissipation based on extreme value statistics can be significantly more accurate than those based on thermodynamic uncertainty ratios, as well as those based on a naive estimator obtained by neglecting nonMarkovian correlations in the Kullback-Leibler divergence of the trajectories of the integrated edge current.

38 pages, 6 figures

References in corpus (12)

• Thermodynamic uncertainty relation for biomolecular processes
• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Lower bounds on dissipation upon coarse graining
• Fundamental Bounds on First Passage Time Fluctuations for Currents
• Hierarchical Bounds on Entropy Production Inferred from Partial Information
• Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit
• Quantum Martingale Theory and Entropy Production
• Estimating Entropy Production Rates with First-Passage Processes
• Skewness and Kurtosis in Stochastic Thermodynamics
• Survival and extreme statistics of work, heat, and entropy production in steady-state heat engines
• Quantum thermodynamics under continuous monitoring: a general framework

Cited by in corpus (12)

• Martingales for physicists: A treatise on stochastic thermodynamics and beyond
• Thermodynamics of computations with absolute irreversibility, unidirectional transitions, and stochastic computation times
• Methods and Conversations in (Post)Modern Thermodynamics
• General theory for localizing the where and when of entropy production meets single-molecule experiments
• Martingale approach for first-passage problems of time-additive observables in Markov processes
• Multicyclic norias: a first-transition approach to extreme values of the currents
• Thermodynamic bounds and symmetries in first-passage problems of fluctuating currents
• Effective Affinity for Generic Currents in Markov Processes
• Work statistics at first-passage times
• From observed transitions to hidden paths in Markov networks
• Compensating random transition-detection blackouts in Markov networks
• Thermodynamic inference in molecular motors: a Martingale approach