Thermodynamic inequalities for molecular fluids

We consider the application of the classical Gibbs inequality for the Helmholtz free energy to a fluid whose potential energy depends on positions and orientations of the constituent molecules. Properties of the given fluid are related to the properties of a corresponding ‘reference’ fluid whose potential is the unweighted orientational average of the given potential. It is shown that Aˇ-A ₀, where A and A ₀ are the free energies respectively of the given and corresponding reference fluids, and that the high temperature limit of A - A ₀ may be either zero or negative infinite, depending on the nature of the potential. As consequences, it is shown that no general inequality exists relating the entropies of these systems, and that the internal energies U and U ₀ are plausibly expected to satisfy Uˇ-U ₀ at sufficiently high temperature. The case for a general inequality relating U and U ₀ is not decided.