Exact Lower Bounds for Some Equilibrium Properties of a Classical One-Component Plasma

It is shown that the internal energy, Helmholtz free energy, and Fourier-transformed static structure factor $S\left(\mathbf{k}\right)$, for a classical electron gas with uniform positive background, are all bounded below by their Debye-Hückel values. This is true whether the equilibrium state is uniform or crystalline and whether periodic or impenetrable-wall boundary conditions are used.