Density-functional theory as an example for the construction of stationarity principles

From the very beginning quantum statistical mechanics can be formulated in terms of a thermodynamic potential, which has the electron density as the basic variable. By employing a well-known procedure in quantum statistical mechanics for the construction of stationarity principles [T. D. Lee and C. N. Yang, Phys. Rev. 113, 1165 (1959); 117, 22 (1960)], the variational principles of Hohenberg, Kohn [P. Hohenberg and W. Kohn, Phys. Rev. B 136, 864 (1964)], and Mermin [N. D. Mermin, Phys. Rev. A 137, 1441 (1965)] are obtained as are generalizations thereof.