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When deriving a master equation for a multipartite weakly-interacting openquantum systems, dissipation is often addressed \textit{locally} on eachcomponent, i.e. ignoring the coherent couplings, which are later added `byhand'. Although simple, the resulting local master equation (LME) is known tobe thermodynamically inconsistent. Otherwise, one may always obtain aconsistent \textit{global} master equation (GME) by working on the energy basisof the full interacting Hamiltonian. Here, we consider a two-node `quantumwire' connected to two heat baths. The stationary solution of the LME and GMEare obtained and benchmarked against the exact result. Importantly, in ourmodel, the validity of the GME is constrained by the underlying secularapproximation. Whenever this breaks down (for resonant weakly-coupled nodes),we observe that the LME, in spite of being thermodynamically flawed: (a)predicts the correct steady state, (b) yields the exact asymptotic heatcurrents, and (c) reliably reflects the correlations between the nodes. Incontrast, the GME fails at all three tasks. Nonetheless, as the inter-nodecoupling grows, the LME breaks down whilst the GME becomes correct. Hence, theglobal and local approach may be viewed as \textit{complementary} tools, bestsuited to different parameter regimes.

Testing the validity of the local and global GKLS master equations on an exactly solvable model