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

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 → 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.