Linearized kinetic-variational theory and short-time kinetic theory

Abstract

We discuss the linearization of the kinetic-variational theory (KVT) II equation for mixtures around absolute equilibrium for a family of pair potentials with hard core and soft tail. In the case of a continuous soft tail, the linear equation reduces to that of Sung and Dahler [J. Chem. Phys. 80, 3025 (1984)], which in turn generalizes to mixtures, the short-time result of Lebowitz, Percus, and Sykes [Phys. Rev. 188, 487 (1969)] that had subsequently been obtained by others using different means. Our equation also represents a generalization of the linearized revised Enskog theory to potentials with attractive tails. Hence, at this level of theory the application of the fundamental technique in the kinetic-variational approach, maximization of entropy subject to constraints, is equivalent to the approaches used by others. However, this technique appears to be more amenable to the production of more general theories. Analysis of the structure of the KVT II theory reveals the necessity of relaxation mechanisms for fluid equilibration that are absent in the various linear theories. These include a mechanism for mixing kinetic and potential energies and a temperature associated with the relaxation of the fluid structure. Various options for these are described and compared. A consistent set of mechanisms provided by a more general class of kinetic-variational theories (KVT III) is discussed. These should serve as a useful guide in improving the alternative approaches that are equivalent to linearized KVT II.