Thermodynamics as an alternative foundation for zero-temperature density functional theory and spin density functional theory

TL;DR

This paper uses thermodynamics to clarify the foundational aspects of zero-temperature density functional theory (DFT) and spin-DFT, revealing inherent ambiguities related to potentials and magnetic fields that were previously overlooked.

Contribution

It demonstrates that thermodynamics provides a clear framework for understanding and resolving ambiguities in zero-temperature DFT and spin-DFT, which were not accessible in standard formulations.

Findings

Charge and spin quantization cause potential indeterminacies.

Potential in empty subspaces is undetermined but irrelevant.

Thermodynamics clarifies foundational ambiguities in zero-temperature DFT.

Abstract

Thermodynamics provides a transparent definition of the free energy of density functional theory (DFT), and of its derivatives - the potentials, at finite temperatures T. By taking the T to 0 limit, it is shown here that both DFT and spin-dependent DFT (for ground states) suffer from precisely the same benign ambiguities: (a) charge and spin quantization lead to "up to a constant" indeterminacies in the potential and the magnetic field respectively, and (b) the potential in empty subspaces is undetermined but irrelevant. Surprisingly, these simple facts were inaccessible within the standard formulation, leading to recent discussions of apparent difficulties within spin-DFT.