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Dwandaru WS, Schmidt M. Variational principle of classical density functional theory via Levy's constrained search method. Phys Rev E Stat Nonlin Soft Matter Phys. 2011;83(6):061133doi: 10.1103/PhysRevE.83.061133.
Dwandaru, W. S., & Schmidt, M. (2011). Variational principle of classical density functional theory via Levy's constrained search method. Physical review. E, Statistical, nonlinear, and soft matter physics, 83(6), 061133. https://doi.org/10.1103/PhysRevE.83.061133
Dwandaru, Wipsar Sunu Brams, and Schmidt, Matthias. "Variational principle of classical density functional theory via Levy's constrained search method." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 83,6 (2011): 061133. doi: https://doi.org/10.1103/PhysRevE.83.061133
Dwandaru WS, Schmidt M. Variational principle of classical density functional theory via Levy's constrained search method. Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6):061133. doi: 10.1103/PhysRevE.83.061133. Epub 2011 Jun 22. PMID: 21797328.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6):061133. doi: 10.1103/PhysRevE.83.061133. Epub 2011 Jun 22.

Variational principle of classical density functional theory via Levy's constrained search method.

Physical review. E, Statistical, nonlinear, and soft matter physics

Wipsar Sunu Brams Dwandaru, Matthias Schmidt

Affiliations

  1. H H Wills Physics Laboratory, University of Bristol, Royal Fort, Bristol, United Kingdom.

PMID: 21797328 DOI: 10.1103/PhysRevE.83.061133

Abstract

We show that classical density functional theory can be based on the constrained search method [M. Levy, Proc. Natl. Acad. Sci. USA 76, 6062 (1979)]. From the Gibbs inequality one first derives a variational principle for the grand potential as a functional of a trial many-body distribution. This functional is minimized in two stages. The first step consists of a constrained search of all many-body distributions that generate a given one-body density. The result can be split into internal and external contributions to the total grand potential. In contrast to the original approach by Mermin and Evans, here the intrinsic Helmholtz free-energy functional is defined by an explicit expression that does not refer to an external potential in order to generate the given one-body density. The second step consists of minimizing with respect to the one-body density. We show that this framework can be applied in a straightforward way to the canonical ensemble.

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