Exact conditions and scaling relations in finite temperature density functional theory

TL;DR

This paper derives exact properties and scaling relations for finite temperature density functional theory, providing foundational constraints that can improve the development of practical approximations for thermodynamic systems.

Contribution

It introduces a coordinate scaling transformation at finite temperature and elucidates its implications for the properties of density functional theory.

Findings

Derivation of exact properties of finite temperature density functionals

Introduction of a finite temperature coordinate scaling transformation

Implications for developing better functional approximations

Abstract

Finite temperature density functional theory provides, in principle, an exact description of the thermodynamical equilibrium of many-electron systems. In practical applications, however, the functionals must be approximated. Efficient and physically meaningful approximations can be developed if relevant properties of the exact functionals are known and taken into consideration as constraints. In this work, derivations of exact properties and scaling relations for the main quantities of finite temperature density functional theory are presented. In particular, a coordinate scaling transformation at finite temperature is introduced and its consequences are elucidated.