A simple derivation of the sohyphen;called Gibbs bound on the Helmholtz free energy is given. Formal lower bounds, analogous to the bounds previously derived by Mansooriet al., allow qualitative comments regarding variational calculations of the equation of state. The theory is applied to binary mixtures, with sufficient conditions for stability of the random mixture relative to that of either of the pure components or to the twohyphen;phase mixture of the same composition as the end result. The conditions are used to determine the stabilities of mixtures of hard spheres and hardhyphen;core molecules with additional square wells and steps.
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