Local in time master equations with memory effects: Applicability and interpretation

TL;DR

This paper clarifies the applicability and interpretation of non-Markovian local in time master equations for quantum and classical systems, addressing misunderstandings and introducing the concept of classical non-Markov chains with negative jump rates.

Contribution

It provides a detailed analysis of the physical meaning of non-Markovian master equations and introduces the classical non-Markov chain concept with negative jump rates.

Findings

Clarified conditions for the physical applicability of non-Markovian master equations

Interpreted negative jump rates as indicators of non-Markovian behavior in classical chains

Extended understanding of memory effects in open quantum systems

Abstract

Non-Markovian local in time master equations give a relatively simple way to describe the dynamics of open quantum systems with memory effects. Despite their simple form, there are still many misunderstandings related to the physical applicability and interpretation of these equations. Here we clarify these issues both in the case of quantum and classical master equations. We further introduce the concept of a classical non-Markov chain signified through negative jump rates in the chain configuration.