  We consider a class of open quantum many-body Lindblad dynamics characterized
by an all-to-all coupling Hamiltonian and by dissipation featuring collective
``state-dependent" rates. The latter encodes local incoherent transitions that
depend on average properties of the system. This type of open quantum dynamics
can be seen as a generalization of classical (mean-field) stochastic Markov
dynamics, in which transitions depend on the instantaneous configuration of the
system, to the quantum domain. We study the time evolution in the limit of
infinitely large systems, and we demonstrate the exactness of the mean-field
equations for the dynamics of average operators. We further derive the
effective dynamical generator governing the time evolution of (quasi-)local
operators. Our results allow for a rigorous and systematic investigation of the
impact of quantum effects on paradigmatic classical models, such as quantum
generalized Hopfield associative memories or (mean-field)
kinetically-constrained models.
