Entropy production and correlations in a controlled non-Markovian setting

TL;DR

This paper investigates how non-Markovian dynamics, correlations, and entropy production are interconnected in a qubit system coupled to a thermal bath and an ancillary qubit, revealing conditions for equilibrium and signatures of non-Markovianity.

Contribution

It introduces a detailed analysis of entropy production and correlations in a controlled non-Markovian setting, highlighting the role of effective temperatures and transient negativity as indicators.

Findings

Coupling induces effective temperatures in the composite system.

Correlations are linked to the emergence of effective temperatures.

Transient negativity of entropy production indicates non-Markovian behavior.

Abstract

We study the relationship between (non-)Markovian evolutions, established correlations, and the entropy production rate. We consider a system qubit in contact with a thermal bath and in addition the system is strongly coupled to an ancillary qubit. We examine the steady state properties finding that the coupling leads to effective temperatures emerging in the composite system, and show that this is related to the creation of correlations between the qubits. By establishing the conditions under which the system reaches thermal equilibrium with the bath despite undergoing a non-Markovian evolution, we examine the entropy production rate, showing that its transient negativity is a sufficient sign of non-Markovianity.