Linear response to perturbation of non-exponential renewal processes

TL;DR

This paper investigates how a two-state renewal process responds to perturbations, revealing that aging effects can suppress the long-term response to coherent stimuli, using a stochastic rate equation framework.

Contribution

It introduces a stochastic rate equation approach to analyze the linear response of renewal processes with aging, highlighting the impact of aging on response behavior.

Findings

Response vanishes in the long-time limit due to aging

A stochastic rate equation equivalent to a master equation is used

Aging causes suppression of response to perturbations

Abstract

We study the linear response of a two-state stochastic process, obeying renewal condition, by means of a stochastic rate equation equivalent to a master equation with infinite memory. We show that the condition of perennial aging makes the response to coherent perturbation vanish in the long-time limit.