Lower bounds for correlation energy of mixtures of charged hard spheres and ionic mixtures in uniform background

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Abstract
A method to obtain exact lower bounds for the correlation energy of one-component plasmas is extended to neutral mixtures of charged hard spheres and to mixtures of point charges in a uniform background of opposite charges. In the former case, upper bounds for the correlation functions of charge densities are derived. These upper bounds, the semipositivity of these functions, and that of the charge-density-fluctuation spectrum are used to improve upon the known bound due to Onsager. In the latter case, the semipositivity of pair-distribution functions and generalizations of Mermin's inequality for the structure factor lead to bounds which improve upon known results in the domain of intermediate coupling.