  We address the real-time dynamics of lattice quantum spin models coupled to
single or multiple Markovian dissipative reservoirs using the method of closed
hierarchies of correlation functions. This approach allows us to solve a number
of quantum spin models exactly in arbitrary dimensions, which is illustrated
explicitly with two examples of driven-dissipative systems. We investigate
their respective nonequilibrium steady states as well as the full real-time
evolution on unprecedented system sizes. Characteristic time scales are derived
analytically, which allows us to understand the nontrivial finite-size scaling
of the dissipative gap. The corresponding scaling exponents are confirmed by
solving numerically for the full real-time evolution of two-point correlation
functions.
