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We consider the effects of strong dissipation in quantum systems with anotion of locality, which induces a hierarchy of many-body relaxationtimescales as shown in [Phys. Rev. Lett. 124, 100604 (2020)]. If the strengthof the dissipation varies strongly in the system, additional separations oftimescales can emerge, inducing a manifold of metastable states, to whichobservables relax first, before relaxing to the steady state. Our simple model,involving one or two "good" qubits with dissipation reduced by a factor$\alpha<1$ compared to the other "bad" qubits, confirms this picture and admitsa perturbative treatment.

Random matrix theory for quantum and classical metastability in local Liouvillians