Macroscopic localization and collective memory in Poisson renewal resetting

TL;DR

This paper demonstrates how Poisson renewal processes can lead to macroscopic localization and collective memory, revealing a discontinuous phase transition in collective dynamics with ecological implications.

Contribution

It introduces an age-structured framework showing localization at reset points and uncovers a novel discontinuous phase transition to collective memory in renewal processes.

Findings

Discrete localization occurs at reset configurations.

A discontinuous transition from stationary to aging dynamics.

Collective interactions can sustain memory despite memoryless resets.

Abstract

Stochastic renewal processes are ubiquitous across physics, biology, and the social sciences. Here, we show that continuous-time renewal dynamics can naturally produce a mixed discrete-continuous structure, with a macroscopic fraction of particles occupying a discrete state. For ensembles of continuous-time random walkers subject to Poissonian renewal resets, we develop an age-structured framework showing this discrete component corresponds to localization at the reset configuration. We next show that collective interactions can retain memory although all reset events are memoryless. Remarkably, the transition to collective memory is discontinuous, and we identify a discontinuous dynamical phase transition from weak collective bias, where the dynamics are stationary, to strong collective bias where the dynamics are nonstationary and display aging up to finite-size effects. We explicitly discuss ecological implications of our work, illustrating how continuous-time renewal dynamics shape macroscopic structure and collective organization with long-term memory.