  A simple fluid, described by point-like particles interacting via the
Lennard-Jones potential, is considered under confinement in a slit geometry
between two walls at distance Lz apart for densities inside the vapor-liquid
coexistence curve. Equilibrium then requires the coexistence of a liquid
"bridge" between the two walls, and vapor in the remaining pore volume. We
study this equilibrium for several choices of the wall-fluid interaction
(corresponding to the full range from complete wetting to complete drying, for
a macroscopically thick film), and consider also the kinetics of state changes
in such a system. In particular, we study how this equilibrium is established
by diffusion processes, when a liquid is inserted into an initially empty
capillary (partial or complete evaporation into vacuum), or when the volume
available for the vapor phase increases. We compare the diffusion constants
describing the rates of these processes in such inhomogeneous systems to the
diffusion constants in the corresponding bulk liquid and vapor phases.
