Title: Testing the validity of the local and global GKLS master equations on an exactly solvable model,
Abstract: When deriving a master equation for a multipartite weakly-interacting open
quantum systems, dissipation is often addressed \textit{locally} on each
component, i.e. ignoring the coherent couplings, which are later added `by
hand'. Although simple, the resulting local master equation (LME) is known to
be thermodynamically inconsistent. Otherwise, one may always obtain a
consistent \textit{global} master equation (GME) by working on the energy basis
of the full interacting Hamiltonian. Here, we consider a two-node `quantum
wire' connected to two heat baths. The stationary solution of the LME and GME
are obtained and benchmarked against the exact result. Importantly, in our
model, the validity of the GME is constrained by the underlying secular
approximation. 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 heat
currents, and (c) reliably reflects the correlations between the nodes. In
contrast, the GME fails at all three tasks. Nonetheless, as the inter-node
coupling grows, the LME breaks down whilst the GME becomes correct. Hence, the
global and local approach may be viewed as \textit{complementary} tools, best
suited to different parameter regimes.