Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes

Abstract

We study the statistics of infima, stopping times and passage probabilities of entropy production in nonequilibrium steady states, and show that they are universal. We consider two examples of stopping times: first-passage times of entropy production and waiting times of stochastic processes, which are the times when a system reaches for the first time a given state. Our main results are: (i) the distribution of the global infimum of entropy production is exponential with mean equal to minus Boltzmann's constant; (ii) we find the exact expressions for the passage probabilities of entropy production to reach a given value; (iii) we derive a fluctuation theorem for stopping-time distributions of entropy production. These results have interesting implications for stochastic processes that can be discussed in simple colloidal systems and in active molecular processes. In particular, we show that the timing and statistics of discrete chemical transitions of molecular processes, such as, the steps of molecular motors, are governed by the statistics of entropy production. We also show that the extreme-value statistics of active molecular processes are governed by entropy production, for example, the infimum of entropy production of a motor can be related to the maximal excursion of a motor against the direction of an external force. Using this relation, we make predictions for the distribution of the maximum backtrack depth of RNA polymerases, which follows from our universal results for entropy-production infima.

arXiv comment30 pages, 13 figures

References in corpus (55)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Brownian motors: noisy transport far from equilibrium
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Artificial Brownian motors: Controlling transport on the nanoscale
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Fluctuation theorem for stochastic dynamics
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Thermodynamic uncertainty relation for biomolecular processes
• Path ensembles averages in systems driven far-from-equilibrium
• Dissipation bounds all steady-state current fluctuations
• The Nonequilibrium Thermodynamics of Small Systems
• Dissipation: The phase-space perspective
• The Fluctuation Theorem as a Gibbs Property
• High-precision test of Landauer's principle in a feedback trap
• Statistical Physics of Self-Replication
• Stochastic thermodynamics under coarse-graining
• Universal bounds on current fluctuations
• Nonequilibrium fluctuations in a resistor
• Test of Jarzynski and Crooks fluctuation relations in an electronic system
• Universal features in the energetics of symmetry breaking
• Thermodynamic costs of information processing in sensory adaption
• Efficiency of cellular information processing
• A fluidized granular medium as an instance of the Fluctuation Theorem
• Entropy production and Kullback-Leibler divergence between stationary trajectories of discrete systems
• Entropy production in full phase space for continuous stochastic dynamics
• Experimental verification of a modified fluctuation-dissipation relation for a micron-sized particle in a non-equilibrium steady state
• Fluctuation Relations for Diffusion Processes
• Tightening the uncertainty principle for stochastic currents
• Measurement of Stochastic Entropy Production
• Symmetries of generating functionals of Langevin processes with colored multiplicative noise
• Decision Making in the Arrow of Time
• Multiple-scale stochastic processes: decimation, averaging and beyond
• Distribution of Entropy Production for a Colloidal Particle in a Nonequilibrium Steady State
• Steady state fluctuation relations for systems driven by an external random force
• Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale
• Jarzynski Relation, Fluctuation Theorems, and Stochastic Thermodynamics for Non-Markovian Processes
• Understanding Mechanochemical Coupling in Kinesins Using First-Passage Time Processes
• Thermodynamics of Error Correction
• Precise Asymptotics for a Random Walker's Maximum
• Nonequilibrium Equalities in Absolutely Irreversible Processes
• Extreme Value Statistics and Traveling Fronts: Various Applications
• Generalized Haldane Equation and Fluctuation Theorem in the Steady State Cycle Kinetics of Single Enzymes
• Entropy Production in Mesoscopic Stochastic Thermodynamics: Nonequilibrium Kinetic Cycles Driven by Chemical Potentials, Temperatures, and Mechanical Forces
• Characterizing Potentials by a Generalized Boltzmann Factor
• Thermodynamic limits to information harvesting by sensory systems
• Waiting for rare entropic fluctuations
• Realization of nonequilibrium thermodynamic processes using external colored noise
• Fluctuations and response in a non-equilibrium micron-sized system
• Test of the fluctuation theorem for stochastic entropy production in a nonequilibrium steady state
• Local Detailed Balance : A Microscopic Derivation
• Conditional reversibility in nonequilibrium stochastic systems
• Decay times in turnover statistics of single enzymes

Cited by in corpus (72)

• Broken detailed balance and non-equilibrium dynamics in living systems
• Irreversibility in active matter systems: Fluctuation theorem and mutual information
• Generic Properties of Stochastic Entropy Production
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
• Stochastic thermodynamics of computation
• Fundamental Bounds on First Passage Time Fluctuations for Currents
• Restart could optimize the probability of success in a Bernoulli trial
• The dissipation-time uncertainty relation
• Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement
• Thermodynamics of Gambling Demons
• Origins and diagnostics of the nonequilibrium character of active systems
• Emergent memory and kinetic hysteresis in strongly driven networks
• Integral Fluctuation Relations for Entropy Production at Stopping Times
• Second law of thermodynamics at stopping times
• Interlacing Relaxation and First-Passage Phenomena in Reversible Discrete and Continuous Space Markovian Dynamics
• Information-theoretical bound of the irreversibility in thermal relaxation processes
• Duality Between Relaxation and First Passage in Reversible Markov Dynamics: Rugged Energy Landscapes Disentangled
• Time-resolved statistics of snippets as general framework for model-free entropy estimators
• Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit
• Kinetic uncertainty relation on first passage time for accumulated current
• Unified formalism for entropy productions and fluctuation relations
• First-passage times in renewal and nonrenewal systems
• Quantum Martingale Theory and Entropy Production
• Exact Distributions of Currents and Frenesy for Markov Bridges
• Universal tradeoff relation between speed, uncertainty, and dissipation in nonequilibrium stationary states
• Universal First-Passage-Time Distribution of Non-Gaussian Currents
• Estimating Entropy Production Rates with First-Passage Processes
• Extreme reductions of entropy in an electronic double dot
• Thermodynamic cost for precision of general counting observables
• Arcsine Laws in Stochastic Thermodynamics
• Counting quantum jumps: a summary and comparison of fixed-time and fluctuating-time statistics in electron transport
• First-Passage Duality
• Thermodynamics of computations with absolute irreversibility, unidirectional transitions, and stochastic computation times
• Methods and Conversations in (Post)Modern Thermodynamics
• Fluctuating Entropy Production on the Coarse-Grained Level: Inference and Localization of Irreversibility
• First Passage Times for Continuous Quantum Measurement Currents
• Non-renewal statistics in quantum transport through the eyes of first-passage and waiting time distributions
• Skewness and Kurtosis in Stochastic Thermodynamics
• Thermodynamic uncertainty relation for quantum first passage process
• Universal Property of the Housekeeping Entropy Production
• Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation
• Progressive quenching - Globally coupled model
• Martingale-induced local invariance in Progressive Quenching
• Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime
• Extremal statistics for a resetting Brownian motion before its first-passage time
• Detailed fluctuation theorem bounds apparent violations of the second law
• Lower bound for entropy production rate in stochastic systems far from equilibrium
• Survival and extreme statistics of work, heat, and entropy production in steady-state heat engines
• Entropy estimation for partially accessible Markov networks based on imperfect observations: Role of finite resolution and finite statistics
• Information bound for entropy production from the detailed fluctuation theorem
• Generalized Continuous Maxwell Demons
• An Information Theoretic Analysis of Sequential Decision-Making
• Entropy production from waiting-time distributions for overdamped Langevin dynamics
• Dispersion of the time spent in a state: General expression for unicyclic model and dissipation-less precision
• Martingale approach for first-passage problems of time-additive observables in Markov processes
• Thermodynamic nature of irreversibility in active matter
• Martingale drift of Langevin dynamics and classical canonical spin statistics
• Effective Affinity for Generic Currents in Markov Processes
• Thermodynamic bounds and symmetries in first-passage problems of fluctuating currents
• Full counting statistics and first-passage times in quantum Markovian processes: Ensemble relations, metastability, and fluctuation theorems
• Work statistics at first-passage times
• Upper bound for the average entropy production based on stochastic entropy extrema
• Time-reversal symmetric Crooks and Gallavotti-Cohen fluctuation relations in driven classical Markovian systems
• Extreme-Value Statistics of Stochastic Transport Processes: Applications to Molecular Motors and Sports
• First-Passage-Time Asymmetry for Biased Run-and-Tumble Processes
• Compensating random transition-detection blackouts in Markov networks
• Lower Bound on Irreversibility in Thermal Relaxation of Open Quantum Systems
• Effective bandwidth of non-Markovian packet traffic
• Thermodynamic inference in molecular motors: a Martingale approach
• Universal trade-off between irreversibility and intrinsic timescale in thermal relaxation with applications to thermodynamic inference
• Quantum thermodynamics under continuous monitoring: a general framework