2011/04/20 by Wipsar Sunu Brams Dwandaru, Matthias Schmidt, Dwandaru, Wipsar Sunu Brams +1
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectroscopy and Quantum Chemical Studies #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1104.3951
openalex publication_date 2011/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that classical density functional theory can be based on the\nconstrained search method [M. Levy, Proc. Natl. Acad. Sci. 76, 6062 (1979)].\nFrom the Gibbs inequality one first derives a variational principle for the\ngrand potential as a functional of a trial many-body distribution. This\nfunctional is minimized in two stages. The first step consists of a constrained\nsearch of all many-body distributions that generate a given one-body density.\nThe result can be split into internal and external contributions to the total\ngrand potential. In contrast to the original approach by Mermin and Evans, here\nthe intrinsic Helmholtz free energy functional is defined by an explicit\nexpression that does not refer to an external potential in order to generate\nthe given one-body density. The second step consists of minimizing with respect\nto the one-body density. We show that this framework can be applied in a\nstraightforward way to the canonical ensemble.\n