  This work is devoted to the exact statistical mechanics treatment of simple
inhomogeneous few-body systems. The system of two Hard Spheres (HS) confined in
a hard spherical pore is systematically analyzed in terms of its dimensionality
>. The canonical partition function, and the one- and two-body distribution
functions are analytically evaluated and a scheme of iterative construction of
the system properties is presented. We analyse in detail both the effect of
high confinement, when particles become caged, and the low density limit. Other
confinement situations are also studied analytically and several relations
between, the two HS in a spherical pore, two sticked HS in a spherical pore,
and two HS on a spherical surface partition functions are traced. These
relations make meaningful the limiting caging and low density behavior. Turning
to the system of two HS in a spherical pore, we also analytically evaluate the
pressure tensor. The thermodynamic properties of the system are discussed. To
accomplish this statement we purposely focus in the overall characteristics of
the inhomogeneous fluid system, instead of concentrate in the peculiarities of
a few body system. Hence, we analyse the equation of state, the pressure at the
wall, and the fluid-substrate surface tension. The consequences of new results
about the spherically confined system of two HS in D dimension on the confined
many HS system are investigated. New constant coefficients involved in the low
density limit properties of the open and closed system of many HS in a
spherical pore are obtained for arbitrary. The complementary system of many HS
which surrounds a hard sphere (a cavity inside of a bulk HS system) is also
discussed.
