  A state of an open quantum system is described by a density matrix, whose
dynamics is governed by a Liouvillian superoperator. Within a general
framework, we explore fundamental properties of both first-order dissipative
phase transitions and second-order dissipative phase transitions associated
with a symmetry breaking. In the critical region, we determine the general form
of the steady-state density matrix and of the Liouvillian eigenmatrix whose
eigenvalue defines the Liouvillian spectral gap. We illustrate our exact
results by studying some paradigmatic quantum optical models exhibiting
critical behavior.
