Statistical mechanics of the uniform electron gas Lewi, Mathieu Lieb, Élliott Seiringer, Robert ; https://orcid.org/0000-0002-6781-0521 ddc:510 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. Ecole Polytechnique 2018 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/180 https://research-explorer.ista.ac.at/download/180/5726 Lewi M, Lieb É, Seiringer R. Statistical mechanics of the uniform electron gas. <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. 2018;5:79-116. doi:<a href="https://doi.org/10.5802/jep.64">10.5802/jep.64</a> eng info:eu-repo/semantics/altIdentifier/doi/10.5802/jep.64 info:eu-repo/semantics/altIdentifier/issn/2429-7100 info:eu-repo/semantics/altIdentifier/e-issn/2270-518X info:eu-repo/semantics/altIdentifier/arxiv/1705.10676 https://creativecommons.org/licenses/by-nd/4.0/ info:eu-repo/semantics/openAccess