Date of Award

12-1-2021

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Physics

Content Description

1 online resource (vi, 57 pages)

Dissertation/Thesis Chair

Ariel AC Caticha

Committee Members

Ariel AC Caticha, Carlo CC Cafaro, Herbert HF Fotso, Oleg OL Lunin, Daniel DR Robbins

Keywords

Contact Structure, Density Functional Theory, Electron Gas, Entropic Inference, Inhomogeneous Fluids, Maximum Entropy, Density functionals, Maximum entropy method, Inhomogeneous materials, Thermodynamic equilibrium, Liquids

Subject Categories

Condensed Matter Physics | Physics | Statistical, Nonlinear, and Soft Matter Physics

Abstract

A unified formulation of the density functional theory is constructed on the foundations of entropic inference in both the classical and the quantum regimes. The theory is introduced as an application of entropic inference for inhomogeneous fluids in thermal equilibrium. It is shown that entropic inference reproduces the variational principle of DFT when informationabout expected density of particles is imposed. In the classical regime, this process introduces a family of trial density-parametrized probability distributions, and consequently a trial entropy, from which the preferred one is found using the method of Maximum Entropy (MaxEnt). In the quantum regime, similarly, the process involves introduction of a family of trial density-parametrized density matrices, and consequently a trial entropy, from which the preferred density matrix is found using the method of quantum MaxEnt. As illustrations some known approximation schemes of the theory are discussed.

Download

Share

COinS