  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.
