Maximum Entropy approach to a Mean Field Theory for Fluids

Abstract

Making statistical predictions requires tackling two problems: one must assign appropriate probability distributions and then one must calculate a variety of expected values. The method of maximum entropy is commonly used to address the first problem. Here we explore its use to tackle the second problem. We show how this use of maximum entropy leads to the Bogoliuvob variational principle which we generalize, apply to density functional theory, and use it to develop a mean field theory for classical fluids. Numerical calculations for Argon gas are compared with experimental data.

Correctly included 4 figures into the article. Presented at MaxEnt 2002, the 22th International Workshop on Bayesian Inference and Maximum Entropy Methods (August 3-7, 2002, Moscow, Idaho, USA)

Cited by in corpus (5)

• Variational Principle of Bogoliubov and Generalized Mean Fields in Many-Particle Interacting Systems
• Entropic criterion for model selection
• Using Relative Entropy to Find Optimal Approximations: an Application to Simple Fluids
• Maximum entropy approach to the theory of simple fluids
• Maximum Entropy and the Variational Method in Statistical Mechanics: an Application to Simple Fluids