{
  "id": "cond-mat/0104390",
  "version": "v1",
  "published": "2001-04-20T12:44:48.000Z",
  "updated": "2001-04-20T12:44:48.000Z",
  "title": "The density functional theory of classical fluids revisited",
  "authors": [
    "J. -M. Caillol"
  ],
  "comment": "10 pages",
  "doi": "10.1088/0305-4470/35/19/301",
  "categories": [
    "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 ${\\cal A}[\\rho]$ is a convex functional of the density $\\rho$. $\\log \\Xi [\\phi]$ and ${\\cal A}[\\rho]$ 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 $\\rho$ is precisely that considered in the density functional theory while the dual principle, which gives ${\\cal A}[\\rho]$ as the maximum of a functional of $\\phi$ seems to be a new result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-04-20T12:44:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "density functional theory",
      "classical fluids",
      "convex functional",
      "variational principle",
      "kohn-sham free energy"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}