Signatures of non-Markovianity in classical single-time probability distributions

TL;DR

This paper demonstrates how the Kolmogorov distance can quantify memory effects in classical stochastic processes by analyzing the evolution of single-time probability distributions, and explores its relation to other non-Markovianity indicators.

Contribution

It introduces the use of Kolmogorov distance as a tool to quantify non-Markovianity in classical processes and compares it with existing signatures.

Findings

Kolmogorov distance effectively quantifies memory effects.

Relation established between Kolmogorov distance and other non-Markovianity signatures.

Provides a framework for analyzing classical non-Markovian dynamics.

Abstract

We show that the Kolmogorov distance allows to quantify memory effects in classical stochastic processes by studying the evolution of the single-time probability distribution. We further investigate the relation between the Kolmogorov distance and other sufficient but not necessary signatures of non-Markovianity within the classical setting.