  A general quantum thermodynamics network is composed of thermal devices
connected to the environments through quantum wires. The coupling between the
devices and the wires may introduce additional decay channels which modify the
system performance with respect to the directly-coupled device. We analyze this
effect in a quantum three-level device connected to a heat bath or to a work
source through a two-level wire. The steady state heat currents are decomposed
into the contributions of the set of simple circuits in the graph representing
the master equation. Each circuit is associated with a mechanism in the device
operation and the system performance can be described by a small number of
circuit representatives of those mechanisms. Although in the limit of weak
coupling between the device and the wire the new irreversible contributions can
become small, they prevent the system from reaching the Carnot efficiency.
