Entropy production versus memory effects in two-level open quantum systems

TL;DR

This paper investigates various definitions of entropy production in two-level open quantum systems, analyzing their relationships with memory effects and demonstrating their behavior across different coupling regimes.

Contribution

It compares multiple entropy production definitions, reveals their equivalences and discrepancies at different coupling strengths, and extends the concept to dynamical maps.

Findings

All definitions coincide at weak coupling.

Discrepancies emerge at strong coupling, but some definitions still match.

A new extended entropy production concept aligns with P-divisibility.

Abstract

We compare several definitions of entropy production rate introduced in the literature from a large variety of situations and motivations, and then analyze their relations with memory effects. Considering a relevant experimental example of a qubit interacting with a single bosonic mode playing the role of a finite bath, we show that all definitions of entropy production coincide at weak coupling. In the strong coupling regime, significant discrepancies emerge between the different entropy production rates, although some similarities in the overall behaviour remain. However, surprisingly, two of these definitions -- one based on local quantities of the system and the other on non-local quantities -- coincide exactly, even in the case of strong coupling. Finally, a high degree of correspondence is observed when memory effects characterized by P-divisibility are compared with the sign of all entropy production rates in the case of weak coupling. Such correspondence degrades at strong coupling, leading us to extend the concept of entropy production to the dynamical map. We show a perfect equivalence between the sign of this enlarged concept of entropy production and P-divisibility, both numerically and analytically, in the case of phase-covariant master equations.