  The problem of construction of a quantum master equation for a system of
sites weakly coupled to each other and to one or more reservoirs (open quantum
network) is considered. Microscopic derivation of a quantum master equation
requires a diagonalization of the Hamiltonian of the network, which can be a
difficult task. When the inter-site couplings are weak, the local approach,
which neglects the influence of the inter-site couplings on the
system-reservoir couplings, is often used. Recently, some doubts were cast to
the consistency of the local approach. We develop a systematic perturbation
expansion to derive corrections to the local approach and establish its range
of validity. Using this extension of the local approach, we derive an
expression for the heat flux for a particular model and show that it does not
violate the second law of thermodynamics.
