Connection formulas for thermal density functional theory

TL;DR

This paper extends the adiabatic connection formula from ground-state to thermal density functional theory, relating correlation energies through temperature integrals and illustrating with the uniform electron gas.

Contribution

It introduces a thermal adiabatic connection formula and relates correlation components via temperature and coupling-constant integrations, advancing theoretical understanding.

Findings

Derived a temperature-based integral formula for thermal DFT.

Connected different correlation components through integrals.

Applied the theory to the uniform electron gas.

Abstract

The adiabatic connection formula of ground-state density functional theory relates the correlation energy to a coupling-constant integral over a purely potential contribution, and is widely used to understand and improve approximations. The corresponding formula for thermal density functional theory is cast as an integral over temperatures instead, ranging upward from the system's physical temperature. We also show how to relate different different correlation components to each other, either in terms of temperature- or coupling-constant integrations. We illustrate our results on the uniform electron gas.