Exact conditions on the temperature dependence of density functionals

TL;DR

This paper derives exact temperature-dependent conditions for density functionals in thermal DFT, showing monotonicity and concavity properties, with implications demonstrated on the Hubbard dimer and uniform gas.

Contribution

It establishes fundamental exact conditions on the temperature dependence of density functionals, linking entropy, free energy, and other key quantities in thermal DFT.

Findings

Entropy and kinetic-electron-electron functionals increase with temperature.

Mermin functional exhibits downward concavity.

Conditions validated on Hubbard dimer and uniform gas.

Abstract

Universal exact conditions guided the construction of most ground-state density functional approximations in use today. We derive the relation between the entropy and Mermin free energy density functionals for thermal density functional theory. Both the entropy and sum of kinetic and electron-electron repulsion functionals are shown to be monotonically increasing with temperature, while the Mermin functional is concave downwards. Analogous relations are found for both exchange and correlation. The importance of these conditions is illustrated in two extremes: the Hubbard dimer and the uniform gas.