Thermodynamic bounds and symmetries in first-passage problems of 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.

arXiv comment55 pages, 8 figures, typos corrected in Eqs. (27), (38), (76), (77), (90), (91), and (160)

References in corpus (44)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The large deviation approach to statistical mechanics
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Thermodynamic uncertainty relation for biomolecular processes
• Dissipation bounds all steady-state current fluctuations
• Fluctuation theorems for stochastic dynamics
• Nonequilibrium Markov processes conditioned on large deviations
• Universal bounds on current fluctuations
• Discrete-time thermodynamic uncertainty relation
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Entropy production and Kullback-Leibler divergence between stationary trajectories of discrete systems
• Lower bounds on dissipation upon coarse graining
• Fundamental Bounds on First Passage Time Fluctuations for Currents
• The dissipation-time uncertainty relation
• Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes
• Decision Making in the Arrow of Time
• Local detailed balance
• Effective thermodynamics for a marginal observer
• Understanding Mechanochemical Coupling in Kinesins Using First-Passage Time Processes
• Exact Coarse Graining Preserves Entropy Production out of Equilibrium
• Effect of a magnetic field on the thermodynamic uncertainty relation
• Generalized Haldane Equation and Fluctuation Theorem in the Steady State Cycle Kinetics of Single Enzymes
• Integral Fluctuation Relations for Entropy Production at Stopping Times
• Second law of thermodynamics at stopping times
• Waiting for rare entropic fluctuations
• Fluctuating observation time ensembles in the thermodynamics of trajectories
• Thermodynamic uncertainty relation for first-passage times on Markov chains
• Mapping of uncertainty relations between continuous and discrete time
• Effective fluctuation and response theory
• Milestoning estimators of dissipation in systems observed at a coarse resolution: When ignorance is truly bliss
• Kinetic uncertainty relation on first passage time for accumulated current
• Unified formalism for entropy productions and fluctuation relations
• Martingales for physicists: A treatise on stochastic thermodynamics and beyond
• Universal tradeoff relation between speed, uncertainty, and dissipation in nonequilibrium stationary states
• Estimating Entropy Production Rates with First-Passage Processes
• First-Passage Duality
• Thermodynamics of computations with absolute irreversibility, unidirectional transitions, and stochastic computation times
• Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation
• An estimator of entropy production for partially accessible Markov networks based on the observation of blurred transitions
• Entropy estimation for partially accessible Markov networks based on imperfect observations: Role of finite resolution and finite statistics
• Martingale approach for first-passage problems of time-additive observables in Markov processes
• Effective Affinity for Generic Currents in Markov Processes
• First-Passage-Time Asymmetry for Biased Run-and-Tumble Processes
• Thermodynamic inference in molecular motors: a Martingale approach

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