  We explore the use of the method of Maximum Entropy (ME) as a technique to
generate approximations. In a first use of the ME method the "exact" canonical
probability distribution of a fluid is approximated by that of a fluid of hard
spheres; ME is used to select an optimal value of the hard-sphere diameter.
These results coincide with the results obtained using the Bogoliuvob
variational method. A second more complete use of the ME method leads to a
better descritption of the soft-core nature of the interatomic potential in
terms of a statistical mixture of distributions corresponding to hard spheres
of different diameters. As an example, the radial distribution function for a
Lennard-Jones fluid (Argon) is compared with results from molecular dynamics
simulations. There is a considerable improvement over the results obtained from
the Bogoliuvob principle.
