Heat current and entropy production rate in local non-Markovian quantum dynamics of global Markovian evolution

TL;DR

This paper investigates how heat current and entropy production behave in non-Markovian quantum dynamics, revealing deficits compared to Markovian cases and their relation to entanglement.

Contribution

It introduces the concepts of heat current deficit and entropy production rate deficit in non-Markovian quantum systems and explores their relation to entanglement.

Findings

Identification of heat current and entropy production deficits in non-Markovian dynamics

Relation between deficits and entanglement measures

Complementarity between heat current deficit and entanglement

Abstract

We examine the elements of the balance equation of entropy in open quantum evolutions and their response as we go from a Markovian to a non-Markovian situation. In particular, we look at the heat current and entropy production rate in the non-Markovian reduced evolution, as well as a Markovian limit of the same, experienced by one of two interacting systems immersed in a Markovian bath. The analysis naturally leads us to define a heat current deficit and an entropy production rate deficit, which are differences between the global and local versions of the corresponding quantities. The investigation leads, in certain cases, to a complementarity of the time-integrated heat current deficit and the relative entropy of entanglement between the two systems.