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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.
Do phenomenological master equations with memory kernel always describe a non-Markovian quantum dynamics characterized by reverse flow of information? Is the integration over the past states of the system an unmistakable signature of non-Markovianity
The study of open quantum systems often relies on approximate master equations derived under the assumptions of weak coupling to the environment. However when the system is made of several interacting subsystems such a derivation is in many cases ver
Local master equations are a widespread tool to model open quantum systems, especially in the context of many-body systems. These equations, however, are believed to lead to thermodynamic anomalies and violation of the laws of thermodynamics. In cont
Master equations are a useful tool to describe the evolution of open quantum systems. In order to characterize the mathematical features and the physical origin of the dynamics, it is often useful to consider different kinds of master equations for t
The quantum master equation is a widespread approach to describing open quantum system dynamics. In this approach, the effect of the environment on the system evolution is entirely captured by the dynamical generator, providing a compact and versatil