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

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 a stronger 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 stronger 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.

8+10 pages, 5+7 figures. Published in Phys. Rev. A 114, 012456 (2026)

arXiv:2601.21930 [quant-ph]

(or arXiv:2601.21930v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2601.21930 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. A 114, 012456 (2026)

https://doi.org/10.1103/s999-8w59 Focus to learn more DOI(s) linking to related resources

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.