Renewal aging and linear response

TL;DR

This paper investigates how aging affects the linear response of renewal processes, revealing that aging can suppress coherent responses or produce slowly decaying signals depending on the approach used.

Contribution

It compares phenomenological and dynamic methods to analyze aging effects on linear response in renewal processes, highlighting differences in predicted responses.

Findings

Aging can eliminate coherent harmonic responses.

Dynamic approach predicts slowly dying out responses.

Steady signals are smaller than phenomenological predictions.

Abstract

We study the linear response to an external perturbation of a renewal process, in an aging condition that, with no perturbation, would yield super-diffusion. We use the phenomenological approach to the linear response adopted in earlier work of other groups, and we find that aging may have the effect of annihilating any sign of coherent response to harmonic perturbation. We also derive the linear response using dynamic arguments and we find a coherent response, although with an intensity dying out very slowly. In the case of a step-like perturbation the dynamic arguments yield in the long-time limit a steady signal whose intensity may be significantly smaller than the phenomenological approach prediction.