Abstract
A variational property of the ground-state energy of an electron gas in an external potential , derived by Hohenberg and Kohn, is extended to nonzero temperatures. It is first shown that in the grand canonical ensemble at a given temperature and chemical potential, no two lead to the same equilibrium density. This fact enables one to define a functional of the density independent of , such that the quantity is at a minimum and equal to the grand potential when is the equilibrium density in the grand ensemble in the presence of .
- Received 8 October 1964
DOI:https://doi.org/10.1103/PhysRev.137.A1441
©1965 American Physical Society