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It is shown that the internal energy, Helmholtz free energy, and Fourier-transformed static structure factor S (k), for a classical electron gas with uniform positive background, are all bounded below by their Debye-H\"uckel values. This is true whether the equilibrium state is uniform or crystalline and whether periodic or impenetrable-wall boundary conditions are used.
N. David Mermin (Fri,) studied this question.
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