Stochastic resetting: A (very) brief review

Abstract

Stochastic processes offer a fundamentally different paradigm of dynamics than deterministic processes, the most prominent example of the latter being Newton's laws of motion. Here, we discuss in a pedagogical manner a simple and illustrative example of stochastic processes in the form of a particle undergoing standard Brownian diffusion, with the additional feature of the particle resetting repeatedly and at random times to its initial condition. Over the years, many different variants of this simple setting have been studied, all of which serve as illustrations of non-trivial and interesting static and dynamic features that characterize stochastic dynamics at long times. We will provide in this work a brief overview of this active and rapidly evolving field by considering the arguably simplest example of Brownian diffusion in one dimension. Along the way, we will learn about some of the general techniques that a physicist employs to study stochastic processes. Relevant to the special issue, we will discuss in detail how introducing resetting in an otherwise diffusive dynamics provides an explicit optimization of the time to locate a target through a special choice of the resetting protocol. We also discuss thermodynamics of resetting, and provide a bird's eye view of some of the recent work in the field of resetting.

v2: significantly expanded, To appear as an Invited Review to "Frontiers in Physics" Special Issue "Thermodynamics and Optimization of Thermal Machines at Microscopic Scales"

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Cited by in corpus (56)

• Restart expedites quantum walk hitting times
• Stochastic resetting in interacting particle systems: A review
• Extreme statistics and spacing distribution in a Brownian gas correlated by resetting
• Universal framework for record ages under restart
• Fick-Jacobs description and first passage dynamics for diffusion in a channel under stochastic resetting
• Reducing mean first passage times with intermittent confining potentials: a realization of resetting processes
• Exact extreme, order and sum statistics in a class of strongly correlated system
• Thermodynamics of computations with absolute irreversibility, unidirectional transitions, and stochastic computation times
• First detection probability in quantum resetting via random projective measurements
• Restart uncertainty relation for monitored quantum dynamics
• Resetting mediated navigation of active Brownian searcher in a homogeneous topography
• Dynamically emergent correlations between particles in a switching harmonic trap
• Current fluctuations in stochastically resetting particle systems
• Instability in the quantum restart problem
• Random walks with stochastic resetting in complex networks: a discrete time approach
• Kuramoto model subject to subsystem resetting: How resetting a part of the system may synchronize the whole of it
• Dynamically emergent correlations in bosons via quantum resetting
• Tight-binding model subject to conditional resets at random times
• Lévy flights and Lévy walks under stochastic resetting
• Resetting by rescaling: exact results for a diffusing particle in one-dimension
• Extremal statistics for a resetting Brownian motion before its first-passage time
• Search with stochastic home-returns can expedite classical first passage under resetting
• Stochastic resetting in discrete-time quantum dynamics: steady states and correlations in few-qubit systems
• Entropy rate of random walks on complex networks under stochastic resetting
• Resonances of recurrence time of monitored quantum walks
• Efficiency of a microscopic heat engine subjected to stochastic resetting
• Comparing the roles of time overhead and spatial dimensions on optimal resetting rate vanishing transitions, in Brownian processes with potential bias and stochastic resetting
• Causality, localization, and universality of monitored quantum walks with long-range hopping
• Manipulating phases in many-body interacting systems with subsystem resetting
• Active particle in a harmonic trap driven by a resetting noise: an approach via Kesten variables
• Dynamically emergent correlations in Brownian particles subject to simultaneous non-Poissonian resetting protocols
• Designing Autonomous Maxwell Demon via Stochastic Resetting
• Partial versus total resetting for Lévy flights in d dimensions: similarities and discrepancies
• Optimization of escape kinetics by reflecting and resetting
• Emerging cost-time Pareto front for diffusion with stochastic return
• Control of spatiotemporal chaos by stochastic resetting
• Ratchet-mediated resetting: Current, efficiency, and exact solution
• Mean first passage time of active fluctuating membrane with stochastic resetting
• Accelerated first detection in discrete-time quantum walks using sharp restarts
• Siegmund duality for physicists: a bridge between spatial and first-passage properties of continuous and discrete time stochastic processes
• Crossover from Anomalous to Normal Diffusion: Ising Model with Stochastic Resetting
• Stationary-state dynamics of interacting phase oscillators in presence of noise and stochastic resetting
• Diffusion with stochastic resetting on a lattice
• Explicit dynamical properties of the Pelikan random map in the chaotic region and at the intermittent critical point towards the non-chaotic region
• Universal criterion for selective outcomes under stochastic resetting
• Resetting induced multimodality
• Replicating a renewal process at random times
• Brownian-motion approach to statistical mechanics: Langevin equations, fluctuations, and timescales
• Proxitaxis: an adaptive search strategy based on proximity and stochastic resetting
• Localization of information driven by stochastic resetting
• The distribution of the maximum of independent resetting Brownian motions
• Asymmetric simple exclusion process on a random comb: Transport properties in the stationary state
• Role of long jumps in Lévy noise induced multimodality
• Exact fluctuation and long-range correlations in a single-file model under resetting
• Tethering effects on first-passage variables of lattice random walks in linear and quadratic focal point potentials
• Experimental evidence for strong emergent correlations between particles in a switching trap