For a three-oscillator chain with two unequal-temperature baths, the local GKSL master equation is numerically closer to the exact dynamics for weak inter-oscillator coupling, while the global equation wins above a temperature-dependent critical coupling.
(56), (57), (76), and (77), M and N have the following form M = M ⊕ M, N = N ⊕ N
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An open harmonic chain: Exact vs global and local reduced dynamics
For a three-oscillator chain with two unequal-temperature baths, the local GKSL master equation is numerically closer to the exact dynamics for weak inter-oscillator coupling, while the global equation wins above a temperature-dependent critical coupling.