  We introduce a class of quantum Markov semigroups describing the evolution of
interacting quantum lattice systems, specified either as generic qudits or as
fermions. The corresponding generators, which include both conservative and
dissipative evolutions, are given by the superposition of local generators in
the Lindblad form. Under general conditions, we show that the associated
infinite volume dynamics is well defined and can be obtained as the strong
limit of the finite volume dynamics. By regarding the interacting evolution as
a perturbation of a non-interacting dissipative dynamics, we further obtain a
quantitative criterion that yields the ergodicity of the quantum Markov
semigroup together with the exponential convergence of local observables. The
analysis is based on suitable a priori bounds on the resolvent equation which
yield quantitive estimates on the evolution of local observables.
