Non-Poisson processes: regression to equilibrium versus equilibrium correlation functions

TL;DR

This paper investigates the response of non-Poisson dichotomous fluctuations causing super-diffusion, revealing conditions under which the Onsager principle breaks down and proposing methods to compute higher-order correlation functions.

Contribution

It introduces a quantum-like Liouville approach to study non-Poisson processes and analyzes the breakdown of the Onsager principle in these systems.

Findings

Breakdown of Onsager principle in non-Poisson fluctuations

Method for analyzing the anti-symmetric component evolution

Guidelines for calculating higher-order correlation functions

Abstract

We study the response to perturbation of non-Poisson dichotomous fluctuations that generate super-diffusion. We adopt the Liouville perspective and with it a quantum-like approach based on splitting the density distribution into a symmetric and an anti-symmetric component. To accomodate the equilibrium condition behind the stationary correlation function, we study the time evolution of the anti-symmetric component, while keeping the symmetric component at equilibrium. For any realistic form of the perturbed distribution density we expect a breakdown of the Onsager principle, namely, of the property that the subsequent regression of the perturbation to equilibrium is identical to the corresponding equilibrium correlation function. We find the directions to follow for the calculation of higher-order correlation functions, an unsettled problem, which has been addressed in the past by means of approximations yielding quite different physical effects.