Tractable Model for Tunable Non-Markovian Dynamics

TL;DR

This paper introduces a minimal, analytically tractable model for non-Markovian dynamics where the current state depends on arbitrary past states, enabling deeper understanding of complex history-dependent processes across various fields.

Contribution

The paper presents a new minimal model for non-Markovian dynamics that allows analytical study of properties like autocorrelations and information measures, filling a gap in tractable models.

Findings

Autocorrelations can fail to reflect true dependencies.

Many properties of the process can be studied analytically.

The model provides insights into history dependence and information metrics.

Abstract

Non-Markovian dynamics are ubiquitous across physics, biology, and engineering. Yet our understanding of non-Markovian processes significantly lags that of simpler Markovian processes, due largely to a lack of tractable models. In this article, we present a minimal model of non-Markovian dynamics in which the current state copies past states with arbitrary history dependence. We show that many properties of this process can be studied analytically, providing insight into the relationships between history dependence, autocorrelations, and information-theoretic metrics like entropy and dynamical information. Strikingly, we find that autocorrelations can fail, even qualitatively, to capture the underlying dependencies. Ultimately, this model serves as a tractable sandbox for exploring non-Markovian dynamics.