Work fluctuations and Jarzynski equality in stochastic resetting

Abstract

We consider the paradigm of an overdamped Brownian particle in a potential well, which is modulated through an external protocol, in the presence of stochastic resetting. Thus, in addition to the short range diffusive motion, the particle also experiences intermittent long jumps which reset the particle back at a preferred location. Due to the modulation of the trap, work is done on the system and we investigate the statistical properties of the work fluctuations. We find that the distribution function of the work typically, in asymptotic times, converges to a universal Gaussian form for any protocol as long as that is also renewed after each resetting event. When observed for a finite time, we show that the system does not generically obey the Jarzynski equality which connects the finite time work fluctuations to the difference in free energy, albeit a restricted set of protocols which we identify herein. In stark contrast, the Jarzynski equality is always fulfilled when the protocols continue to evolve without being reset. We present a set of exactly solvable models, demonstrate the validation of our theory and carry out numerical simulations to illustrate these findings. Finally, we have pointed out possible realistic implementations for resetting in experiments using the so-called engineered swift equilibration.

7 pages

References in corpus (54)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The large deviation approach to statistical mechanics
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Shortcuts to adiabaticity: concepts, methods, and applications
• Diffusion with Stochastic Resetting
• Stochastic thermodynamics: Principles and perspectives
• Brownian Carnot engine
• Diffusion with Optimal Resetting
• Optimal finite-time processes in stochastic thermodynamics
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• First Passage Under Restart
• First order transition for the optimal search time of Lévy flights with resetting
• Thermodynamics of a Colloidal Particle in a Time-Dependent Non-Harmonic Potential
• Rare events and the convergence of exponentially averaged work values
• Optimal stochastic restart renders fluctuations in first passage times universal
• Diffusion under time-dependent resetting
• Diffusion in a potential landscape with stochastic resetting
• An experimental test of the Jarzynski equality in a mechanical experiment
• Test of Jarzynski and Crooks fluctuation relations in an electronic system
• Dynamical transition in the temporal relaxation of stochastic processes under resetting
• Fluctuation theorem in quantum heat conduction
• Non-equilibrium steady states of stochastic processes with intermittent resetting
• Fluctuating interfaces subject to stochastic resetting
• First passage under stochastic resetting in an interval
• Work fluctuation theorems for harmonic oscillators
• Engineered swift equilibration of a Brownian particle
• Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics
• Stochastic thermodynamics of resetting
• Experimental verification of a modified fluctuation-dissipation relation for a micron-sized particle in a non-equilibrium steady state
• Work and heat probability distribution of an optically driven Brownian particle: Theory and experiments
• Experimental free energy measurements of kinetic molecular states using fluctuation theorems
• Restart could optimize the probability of success in a Bernoulli trial
• Large deviations for Markov processes with resetting
• Experimental test of the differential fluctuation theorem and a generalized Jarzynski equality for arbitrary initial states
• Landau theory of restart transitions
• Steady state fluctuation relations for systems driven by an external random force
• First passage under restart with branching
• Integral Fluctuation Theorems for Stochastic Resetting Systems
• Symmetric Exclusion Process under Stochastic Resetting
• Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement
• Diffusion with stochastic resetting is invariant to return speed
• Invariants of motion with stochastic resetting and space-time coupled returns
• Stochastic resetting in underdamped Brownian motion
• Properties of additive functionals of Brownian motion with resetting
• Experimental evidence of non-Gaussian fluctuations near a critical point
• Work and dissipation fluctuations near the stochastic resonance of a colloidal particle
• Phase transition in protocols minimizing work fluctuations
• Stationary and transient Fluctuation Theorems for effective heat flux between hydrodynamically coupled particles in optical traps
• Work fluctuations for a Brownian particle in a harmonic trap with fluctuating locations
• Experimental measurement of binding energy, selectivity and allostery using fluctuation theorems
• Optimal work in a harmonic trap with bounded stiffness
• Irreversibility to Reversibility Crossover in Transient Response of an Optically Trapped Particle

Cited by in corpus (65)

• Stochastic Resetting and Applications
• Experimental realization of diffusion with stochastic resetting
• Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
• Stochastic resetting: A (very) brief review
• The inspection paradox in stochastic resetting
• Diffusion with resetting in a logarithmic potential
• Stochastic resetting with stochastic returns using external trap
• Ising model with stochastic resetting
• First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
• Geometric Brownian Motion under Stochastic Resetting: A Stationary yet Non-ergodic Process
• Thermodynamic uncertainty relation for systems with unidirectional transitions
• Extremal statistics for stochastic resetting systems
• Occupation time of a run-and-tumble particle with resetting
• Entropy production in systems with unidirectional transitions
• Random acceleration process under stochastic resetting
• Resetting with stochastic return through linear confining potential
• Thermodynamic uncertainty relation for first-passage times on Markov chains
• Diffusion with Local Resetting and Exclusion
• Resetting transition is governed by an interplay between thermal and potential energy
• Random walks on complex networks with first-passage resetting
• Asymmetric Stochastic Resetting: Modeling Catastrophic Events
• Thermodynamic cost of finite-time stochastic resetting
• Universal framework for record ages under restart
• Mitigating long transient time in deterministic systems by resetting
• Work fluctuations for diffusion dynamics submitted to stochastic return
• Tighter thermodynamic bound on speed limit in systems with unidirectional transitions
• Non-equilibrium thermodynamics of diffusion in fluctuating potentials
• First passage of a diffusing particle under stochastic resetting in bounded domains with spherical symmetry
• Random walks on complex networks under node-dependent stochastic resetting
• Restart uncertainty relation for monitored quantum dynamics
• Random walks on complex networks under time-dependent stochastic resetting
• A Unified Approach to Gated Reactions on Networks
• First passage time and information of a one-dimensional Brownian particle with stochastic resetting to random positions
• Rate enhancement of gated drift-diffusion process by optimal resetting
• First-passage functionals for Ornstein Uhlenbeck process with stochastic resetting
• Random walks on complex networks with multiple resetting nodes: a renewal approach
• Dynamics of closed quantum systems under stochastic resetting
• Non-linear diffusion with stochastic resetting
• Effect of stochastic resetting on Brownian motion with stochastic diffusion coefficient
• Extremal statistics for a resetting Brownian motion before its first-passage time
• Branching processes with resetting as a model for cell division
• Fluctuations and stability of a fast driven Otto cycle
• Stochastic resetting with refractory periods: pathway formulation and exact results
• Entropy rate of random walks on complex networks under stochastic resetting
• Search with stochastic home-returns can expedite classical first passage under resetting
• Target Search Optimization by Threshold Resetting
• First passage in discrete-time absorbing Markov chains under stochastic resetting
• Optimal conditions for first passage of jump processes with resetting
• Efficiency of a microscopic heat engine subjected to stochastic resetting
• Optimal resetting strategies for search processes in heterogeneous environments
• Random resetting in search problems
• Designing Autonomous Maxwell Demon via Stochastic Resetting
• Ratchet-mediated resetting: Current, efficiency, and exact solution
• Emerging cost-time Pareto front for diffusion with stochastic return
• Thermodynamic cost of Brownian computers in the stochastic thermodynamics of resetting
• Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: Experiments, theory and numerical tests
• Continuous Gated First-Passage Processes
• Drift-diffusive resetting search process with stochastic returns: speed-up beyond optimal instantaneous return
• Reaction-Path Statistical Mechanics of Enzymatic Kinetics
• Autocorrelation functions and ergodicity in diffusion with stochastic resetting
• Work statistics at first-passage times
• Semi-Markov Processes in Open Quantum Systems. II. Counting Statistics with Resetting
• Stationary state of harmonic chains driven by boundary resetting
• Inducing and optimizing Markovian Mpemba effect with stochastic reset
• Poissonian resetting of subdiffusion in a linear potential