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Thermodynamics provides a transparent definition of the free energy ofdensity functional theory (DFT), and of its derivatives - the potentials, atfinite temperatures T. By taking the T to 0 limit, it is shown here that bothDFT and spin-dependent DFT (for ground states) suffer from precisely the samebenign 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, leadingto recent discussions of apparent difficulties within spin-DFT.Comment: RevTeX, to appear in Phys. Rev.

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