Non-Poisson dichotomous noise: higher-order correlation functions and aging

TL;DR

This paper investigates how non-Poissonian two-state noise affects higher-order correlations and aging phenomena, revealing breakdowns in traditional assumptions and establishing conditions for accurate diffusion modeling.

Contribution

It connects non-exponential waiting times with aging and correlation breakdowns, providing conditions for correct diffusion process descriptions.

Findings

Breakdown of high-order correlation factorization with non-exponential waiting times

Emergence of aging effects in non-Poisson dichotomous noise

Liouville-like approach conditions for accurate diffusion modeling

Abstract

We study a two-state symmetric noise, with a given waiting time distribution $\psi (\tau)$, and focus our attention on the connection between the four-time and the two-time correlation functions. The transition of $\psi (\tau)$ from the exponential to the non-exponential condition yields the breakdown of the usual factorization condition of high-order correlation functions, as well as the birth of aging effects. We discuss the subtle connections between these two properties, and establish the condition that the Liouville-like approach has to satisfy in order to produce a correct description of the resulting diffusion process.