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We explore the relaxation dynamics of quantum many-body systems that undergopurely dissipative dynamics through non-classical jump operators that canestablish quantum coherence. Our goal is to shed light on the differences inthe relaxation dynamics that arise in comparison to systems evolving viaclassical rate equations. In particular, we focus on a scenario where bothquantum and classical dissipative evolution lead to a stationary state with thesame values of diagonal or "classical" observables. As a basis for illustratingour ideas we use spin systems whose dynamics becomes correlated and complex dueto dynamical constraints, inspired by kinetically constrained models (KCMs) ofclassical glasses. We show that in the quantum case the relaxation can beorders of magnitude slower than the classical one due to the presence ofquantum coherences. Aspects of these idealized quantum KCMs become manifest ina strongly interacting Rydberg gas under electromagnetically inducedtransparency (EIT) conditions in an appropriate limit. Beyond revealing a linkbetween this Rydberg gas and the rather abstract dissipative KCMs of quantumglassy systems, our study sheds light on the limitations of the use ofclassical rate equations for capturing the non-equilibrium behavior of thismany-body system.

Out-of-equilibrium evolution of kinetically constrained many-body quantum systems under purely dissipative dynamics