  We present a general approach to derive Lindblad master equations for a
subsystem whose dynamics is coupled to dissipative bosonic modes. The
derivation relies on a Schrieffer-Wolff transformation which allows to
eliminate the bosonic degrees of freedom after self-consistently determining
their state as a function of the coupled quantum system. We apply this
formalism to the dissipative Dicke model and derive a Lindblad master equation
for the atomic spins, which includes the coherent and dissipative interactions
mediated by the bosonic mode. This master equation accurately predicts the
Dicke phase transition and gives the correct steady state. In addition, we
compare the dynamics using exact diagonalization and numerical integration of
the master equation with the predictions of semiclassical trajectories. We
finally test the performance of our formalism by studying the relaxation of a
NOON state and show that the dynamics captures quantum metastability beyond the
mean-field approximation.

Quantum Physics;Quantum Gases