  Although density functional theory provides reliable predictions for the
static properties of simple fluids under confinement, a theory of comparative
accuracy for the transport coefficients has yet to emerge. Nonetheless, there
is evidence that knowledge of how confinement modifies static behavior can aid
in forecasting dynamics. Specifically, molecular simulation studies have shown
that the relationship between excess entropy and self diffusivity of a bulk
equilibrium fluid changes only modestly when the fluid is isothermally
confined, indicating that knowledge of the former might allow semi-quantitative
predictions of the latter. Do other static measures, such as those that
characterize free or available volume, also strongly correlate with
single-particle dynamics of confined fluids? Here, we study this issue for both
the single-component hard-sphere fluid and hard-sphere mixtures. Specifically,
we use molecular simulations and fundamental measure theory to study these
systems at approximately $10^3$ equilibrium state points. We examine three
different confining geometries (slit pore, square channel, and cylindrical
pore) and the effects of packing fraction and particle-boundary interactions.
Although density fails to predict some key qualitative trends for the dynamics
of confined fluids, we find that a new generalized measure of available volume
for inhomogeneous fluids strongly correlates with the self diffusivity across a
wide parameter space in these systems, approximately independent of the degree
of confinement. An important consequence, which we demonstrate here, is that
density functional theory predictions of this static property can be used
together with knowledge of bulk fluid behavior to estimate the diffusion
coefficient of confined fluids under equilibrium conditions.
