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.

arXiv commentv2: 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
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• Dynamically emergent correlations between particles in a switching harmonic trap
• Current fluctuations in stochastically resetting particle systems
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