Thermodynamic Sum Rules for Mixtures of Charged Particles

Several methods to derive thermodynamic sum rules for a system including charged particle are proposed and applied to charged mixtures as well as one-component systems. The validity of the statements is examined carefully with respect to the ordering in the powers of the wave number. As for the mixture of electrons and ions, it is shown how the aspect of the one-component plasma or the ionic mixture appears when electrons become strongly degenerate.