Local H-Theorem for a Kinetic Variational Theory

A long-standing problem in the kinetic theory of fluids at moderate and high densities is how to treat the effect of a range of molecular interaction that extends beyond the nearly impenetrable repulsive core that can reasonably be modeled as a hard-sphere core. The most obvious complications in this connection are as follows. First, for high densities, particles are most of the time interacting with several other particles simultaneously and it is typically not possible to represent the evolution of the system in terms of a sequence of binary collisions. Next, the potential energy density is not determined by the one-particle distribution function alone, and therefore even on the simplest level of approximation the one-particle distribution function alone is not sufficient to describe the state of the system. A possible way of dealing with these difficulties was considered recently by Karkheck et a/. (1) as part of a program proposed by Stell and co-workers to extend the Enskog theory in a way that takes into account the effect of the extended range of interactions. Following the terminology of Stell et aL (z) we will refer to the theory investigated by Karkheck et al.