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A general quantum thermodynamics network is composed of thermal devicesconnected to the environments through quantum wires. The coupling between thedevices and the wires may introduce additional decay channels which modify thesystem performance with respect to the directly-coupled device. We analyze thiseffect in a quantum three-level device connected to a heat bath or to a worksource through a two-level wire. The steady state heat currents are decomposedinto the contributions of the set of simple circuits in the graph representingthe master equation. Each circuit is associated with a mechanism in the deviceoperation and the system performance can be described by a small number ofcircuit representatives of those mechanisms. Although in the limit of weakcoupling between the device and the wire the new irreversible contributions canbecome small, they prevent the system from reaching the Carnot efficiency.

Performance of continuous quantum thermal devices indirectly connected to environments