Abstract
The maximum-entropy principle is used to generalize the variational principle for the ground state (Rayleigh-Ritz minimization principle) to ensembles of unequally weighted states. A hierarchy of nested inequalities for the associated ``free energies'' is deduced. Applications of these inequalities to the estimation of the highest multiplet energy and a generalization of density-functional theory to ensembles of quantum states are discussed. Previous results given in the literature are obtained as special cases of our results under isothermal and adiabatic optimizations.
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