2018/11/30 by Somrita Ray, Debasish Mondal, Shlomi Reuveni
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advection #Computer science #Diffusion #Diffusion and Search Dynamics #Diffusion process #Mathematics #Mechanics #Phase transition #Physics #Process (computing) #Speedup #Statistical physics #Stochastic processes and statistical mechanics #Thermodynamics #Transition point #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1751-8121/ab1fcc
published as Journal of Physics A: Mathematical and Theoretical, 52(25), p.255002, 2019 · 10 Pages, 10 Figures
openalex publication_date 2019/05/07 · arxiv created 2019/05/12 · arxiv updated 2020/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract First-passage processes can be divided in two classes: those that are accelerated by the introduction of restart and those that display an opposite response. In physical systems, a transition between the two classes may occur as governing parameters are varied to cross a universal tipping point. However, a fully tractable model system to teach us how this transition unfolds is still lacking. To bridge this gap, we quantify the effect of stochastic restart on the first-passage time of a drift-diffusion process to an absorbing boundary. There, we find that the transition is governed by the Péclet number ( Pe )—the ratio between the rates of advective and diffusive transport. When Pe > 1 the process is drift-controlled and restart can only hinder its completion. In contrast, when the process is diffusion-controlled and restart can speed-up its completion by a factor of ∼1/ Pe . Such speedup occurs when the process is restarted at an optimal rate , where stands for the optimal restart rate in the pure-diffusion limit. The transition considered herein stands at the core of restart phenomena and is relevant to a large variety of processes that are driven to completion in the presence of noise. Each of these processes has unique characteristics, but our analysis reveals that the restart transition resembles other phase transitions—some of its central features are completely generic.