# Statistical Mechanics of the Uniform Electron Gas

## TL;DR

This paper introduces and analyzes the classical and quantum Uniform Electron Gas models, exploring their properties and relevance in density functional theory, especially in the limit of slowly varying densities.

## Contribution

It defines the classical UEG, distinguishes it from Jellium, and constructs the quantum UEG, providing a comprehensive theoretical framework.

## Key findings

- Classical UEG minimizes indirect Coulomb energy in DFT
- Quantum UEG constructed and compared to classical model
- Insights into low-density behavior of quantum UEG

## Abstract

In this paper we define and study the classical Uniform Electron Gas (UEG), a system of infinitely many electrons whose density is constant everywhere in space. The UEG is defined differently from Jellium, which has a positive constant background but no constraint on the density. We prove that the UEG arises in Density Functional Theory in the limit of a slowly varying density, minimizing the indirect Coulomb energy. We also construct the quantum UEG and compare it to the classical UEG at low density.