  We investigate the critical behavior, both in space and time, of the wetting
interface within the coexistence region around the first-order phase transition
of a fully-connected quantum Ising model in slab geometry. For that, we employ
the Lindblad master equation formalism in which temperature is inherited by the
coupling to a dissipative bath, rather than being a functional parameter as in
the conventional Cahn's free energy. Lindblad's approach gives not only access
to the dissipative dynamics and steady-state configuration of the quantum
wetting interface throughout the whole phase diagram but also shows that the
wetting critical behavior can be successfully exploited to characterize the
phase diagram as an alternative to the direct evaluation of the free energies
of the competing phases.
