P. Tarazona et Y. Rosenfeld, FROM ZERO-DIMENSION CAVITIES TO FREE-ENERGY FUNCTIONALS FOR HARD DISKS AND HARD-SPHERES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 55(5), 1997, pp. 4873-4876
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 cavit
y 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.