Abstract
It is shown that the variational principle for the grand potential of a nonuniform fluid as a functional of the singlet density yields the potential distribution theory for the equilibrium density. We derive the explicit form that the functional takes for a system of hard rods, and propose an approximate one for hard spheres. Attractive interactions are also considered in mean-field approximation. In all cases the pair direct correlation function of the nonuniform system is obtained and the density gradient expansion of the free energy is investigated.
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Robledo, A., Varea, C. On the relationship between the density functional formalism and the potential distribution theory for nonuniform fluids. J Stat Phys 26, 513–525 (1981). https://doi.org/10.1007/BF01011432
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DOI: https://doi.org/10.1007/BF01011432