The explicit density functional and its connection with entropy maximization

The intrinsic Helmholtz free energy, commonly used as a basis for density functional 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 potential For a given pail correlation function, and the pair correlation function ibr a given pair potential. The physical meaning of the density functional is established within the context of a new derivation of statistical mechanics based on entropy th;lt supplies a variational principle for equilibrium by generalizing the thermodynamic potential to nonequlibrium states. This shows that the conventional density functional determines not only the equilibrium density, but also the probability of fluctuations about that density.