  We study the phonon dynamics in lattices of optomechanical resonators where
the mutually coupled photonic modes are coherently driven and the mechanical
resonators are uncoupled and connected to independent thermal baths. We present
a general procedure to obtain the effective Lindblad dynamics of the phononic
modes for an arbitrary lattice geometry, where the light modes play the role of
an effective reservoir that mediates the phonon nonequilibrium dynamics. We
show how to stabilize stationary states exhibiting directional heat currents
over arbitrary distance, despite the absence of thermal gradient and of direct
coupling between the mechanical resonators.
