Statistical mechanics of two hard spheres in a box

We investigate some statistical mechanical properties of a system consisting of two hard spheres in a D-dimensional rectangular box (D=1,2,...). We give a theoretical method for computing a configurational partition function Z(c,D) of this system and compare the equation of state obtained from Z(c,D) with molecular dynamics simulations. Especially in D=3, we give a fully analytic expression for the pressure which turns out to have one or more negative compressibility regions when the box size is small.