The explicit density functional and its connection with entropy maximization

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.