  The equilibrium density distribution and thermodynamic properties of a
Lennard-Jones fluid confined to nano-sized spherical cavities at constant
chemical potential was determined using Monte Carlo simulations. The results
describe both a single cavity with semipermeable walls as well as a collection
of closed cavities formed at constant chemical potential. The results are
compared to calculations using classical Density Functional Theory (DFT). It is
found that the DFT calculations give a quantitatively accurate description of
the pressure and structure of the fluid. Both theory and simulation show the
presence of a ``reverse'' liquid-vapor transition whereby the equilibrium state
is a liquid at large volumes but becomes a vapor at small volumes.
