Markovian master equations for quantum thermal machines: local vs global approach

TL;DR

This paper compares local and global master equations for quantum thermal machines, showing that the local approach is valid at weak coupling and the global approach at strong coupling, based on exact solutions.

Contribution

It provides a detailed comparison and validity regimes for local versus global master equations in quantum thermal machines, clarifying their applicability.

Findings

Local approach is justified at weak coupling.

Global approach is preferable at strong coupling.

Both approaches agree at intermediate coupling.

Abstract

The study of quantum thermal machines, and more generally of open quantum systems, often relies on master equations. Two approaches are mainly followed. On the one hand, there is the widely used, but often criticized, local approach, where machine sub-systems locally couple to thermal baths. On the other hand, in the more established global approach, thermal baths couple to global degrees of freedom of the machine. There has been debate as to which of these two conceptually different approaches should be used in situations out of thermal equilibrium. Here we compare the local and global approaches against an exact solution for a particular class of thermal machines. We consider thermodynamically relevant observables, such as heat currents, as well as the quantum state of the machine. Our results show that the use of a local master equation is generally well justified. In particular, for weak inter-system coupling, the local approach agrees with the exact solution, whereas the global approach fails for non-equilibrium situations. For intermediate coupling, the local and the global approach both agree with the exact solution and for strong coupling, the global approach is preferable. These results are backed by detailed derivations of the regimes of validity for the respective approaches.