  We study the driven-dissipative dynamics of photons interacting with an array
of micromechanical membranes in an optical cavity. Periodic membrane driving
and phonon creation result in an effective photon-number conserving non-unitary
dynamics, which features a steady state with long-range photonic coherence. If
the leakage of photons out of the cavity is counteracted by incoherent driving
of the photonic modes, we show that the system undergoes a dynamical phase
transition to the state with long-range coherence. A minimal system, composed
of two micromechanical membranes in a cavity, is studied in detail, and it is
shown to be a realistic setup where the key processes of the driven-dissipative
dynamics can be seen.
