From zero-dimension cavities to free-energy functionals for hard disks and hard spheres

We present a systematic approach to derive fundamental-measure theory free-energy functionals for hard disks and hard spheres, entirely from the exact free energy in the zero-dimensional limit of a narrow cavity which cannot hold more than one molecule. The functionals are within the generic class that includes the previous successful versions, but have the remarkable property to yield the exact functional for quasi-one-dimensional density distributions.