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The density functional theory of classical fluids revisited | | J.-M. Caillol
; | | Date: |
20 Apr 2001 | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | 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 $log Xi [phi]$ is a convex functional of the external potential $phi$ it is shown that the Kohn-Sham free energy ${cal A}[
ho]$ is a convex functional of the density $
ho$. $log Xi [phi]$ and ${cal A}[
ho]$ 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 unicity of the solution in both cases. The variational principle which gives $log Xi [phi]$ as the maximum of a functional of $
ho$ is precisely that considered in the density functional theory while the dual principle, which gives ${cal A}[
ho]$ as the maximum of a functional of $phi$ seems to be a new result. | | Source: | arXiv, cond-mat/0104390 | | Services: | Forum | Review | PDF | Favorites | |
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