The intrinsic Helmholtz free energy, commonly used as a basis for density f
unctional theories, is here given explicitly as a cluster diagram expansion
with density field points, Also given are explicit variational procedures
For determining the chemical potential for a given density, the pair potent
ial For a given pail correlation function, and the pair correlation functio
n ibr a given pair potential. The physical meaning of the density functiona
l is established within the context of a new derivation of statistical mech
anics based on entropy th;lt supplies a variational principle for equilibri
um by generalizing the thermodynamic potential to nonequlibrium states. Thi
s shows that the conventional density functional determines not only the eq
uilibrium density, but also the probability of fluctuations about that dens
ity.