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The problem of construction of a quantum master equation for a system ofsites weakly coupled to each other and to one or more reservoirs (open quantumnetwork) is considered. Microscopic derivation of a quantum master equationrequires a diagonalization of the Hamiltonian of the network, which can be adifficult task. When the inter-site couplings are weak, the local approach,which neglects the influence of the inter-site couplings on thesystem-reservoir couplings, is often used. Recently, some doubts were cast tothe consistency of the local approach. We develop a systematic perturbationexpansion to derive corrections to the local approach and establish its rangeof validity. Using this extension of the local approach, we derive anexpression for the heat flux for a particular model and show that it does notviolate the second law of thermodynamics.

Perturbative treatment of inter-site couplings in the local description of open quantum networks