Beyond average: heterogeneous first-passage dynamics in many-particle systems with resetting

TL;DR

This paper investigates how collective stochastic resetting influences first-passage times in many-particle systems, revealing broad, heavy-tailed distributions and heterogeneity in absorption times.

Contribution

It introduces a collective resetting protocol based on the most extreme particle and analyzes its effects on first-passage dynamics through simulations.

Findings

Resetting causes broad, heavy-tailed distributions of arrival times.

Mean arrival time diverges beyond a certain resetting rate.

Strong heterogeneity exists in individual particle absorption times.

Abstract

We study how stochastic resetting affects first-passage processes in systems of many interacting particles. While resetting is well understood for single-particle dynamics, its consequences for collective behavior remain less clear. We consider a protocol in which all surviving particles are reset to the position of the most extreme one, motivated by problems in artificial selection and avoidance. Using stochastic simulations of particles diffusing in a confining potential with an absorbing boundary, we examine two notions of arrival: when the first particle reaches the boundary and the point at which half of the particles do. We find that resetting produces broad distributions of arrival times with heavy tails and extended plateaus that span several orders of magnitude. As the resetting rate increases, the mean arrival time grows and diverges beyond a threshold. Trajectory-level analysis also reveals strong heterogeneity, with very short and very long absorption times. These results show that collective resetting lacks a single characteristic time scale and that the definition of arrival is crucial for understanding and controlling such systems.