The density functional theory of classical fluids revisited

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Abstract
We reconsider the density functional theory of nonuniform classical fluids from the point of view of convex analysis. From the observation that the logarithm of the grand-partition function log Ξ[] is a convex functional of the external potential it is shown that the Kohn–Sham free energy [ρ] is a convex functional of the density ρ. log Ξ[] and [ρ] constitute a pair of Legendre transforms and each of these functionals can therefore be obtained as the solution of a variational principle. The convexity ensures the uniqueness of the solution in both cases. The variational principle which gives log Ξ[] as the maximum of a functional of ρ is precisely that considered in the density functional theory while the dual principle, which gives [ρ] as the maximum of a functional of , seems to be a new result.
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