标题： 经典密度泛函理论的变分原理通过 Levy 的约束搜索方法 显示英文标题

标题： Variational Principle of Classical Density Functional Theory via Levy's Constrained Search Method

摘要： 我们证明经典密度泛函理论可以基于约束搜索方法 [M. Levy, Proc. Natl. Acad. Sci. 76, 6062 (1979)]。 从吉布斯不等式出发，首先推导出一个变分原理，该原理将巨势作为试验多体分布的泛函。 这个泛函分为两个阶段进行最小化。 第一步是对所有生成给定单体密度的多体分布进行约束搜索。 结果可以分为总巨势的内部分量和外部分量。 与 Mermin 和 Evans 的原始方法不同，这里的内禀亥姆霍兹自由能泛函由一个显式表达式定义，该表达式不涉及外部势以生成给定的单体密度。 第二步是对单体密度进行最小化。 我们证明这个框架可以直接应用于正则系综。 显示英文摘要

摘要： We show that classical density functional theory can be based on the constrained search method [M. Levy, Proc. Natl. Acad. Sci. 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.