Correlation function and generalized master equation of arbitrary age

TL;DR

This paper investigates a two-state process with non-Poisson waiting times, exploring how aging affects correlation functions using three different theoretical approaches, advancing understanding of non-Markovian dynamics.

Contribution

It compares three methods—Generalized Master Equation, Liouville-like, and trajectory perspective—to define correlation functions for aged non-Poisson processes.

Findings

Aging influences correlation functions in non-Poisson processes.

Different theoretical approaches yield consistent descriptions of aging effects.

The study enhances understanding of non-Markovian stochastic dynamics.

Abstract

We study a two-state statistical process with a non-Poisson distribution of sojourn times. In accordance with earlier work, we find that this process is characterized by aging and we study three different ways to define the correlation function of arbitrary age of the corresponding dichotomous fluctuation based respectively on the Generalized Master Equation formalism, on a Liouville-like approach and on a trajectory perspective.