A kinetic mean-field theory for the evolution of the one-particle distribution function is derived from maximizing the entropy. For a potential with a hard-sphere core plus tail, the resulting theory treats the hard-core part as in the revised Enskog theory. The tail, weighted by the hard-sphere pair distribution function, appears linearly in a mean-field term. The kinetic equation is accompanied by an entropy functional for which an H theorem was proven earlier. The revised Enskog theory is obtained by setting the potential tail to zero, the Vlasov equation is obtained by setting the hard-sphere diameter to zero, and an equation of the Enskog–Vlasov type is obtained by effecting the Kac limit on the potential tail. At equilibrium, the theory yields a radial distribution function that is given by the hard-sphere reference system and thus furnishes through the internal energy a thermodynamic description which is exact to first order in inverse temperature. A second natural route to thermodynamics (from the momentum flux which yields an approximate equation of state) gives somewhat different results; both routes coincide and become exact in the Kac limit. Our theory furnishes a conceptual basis for the association in the heuristically based modified Enskog theory (MET) of the contact value of the radial distribution function with the ’’thermal pressure’’ since this association follows from our theory (using either route to thermodynamics) and moreover becomes exact in the Kac limit. Our transport theory is readily extended to the general case of a soft repulsive core, e.g., as exhibited by the Lennard-Jones potential, via by-now-standard statistical–mechanical methods involving an effective hard-core potential, thus providing a self-contained statistical–mechanical basis for application to such potentials that is lacking in the standard versions of the MET. We obtain very good agreement with experiment for the thermal conductivity and shear viscosity of several saturated simple liquids.

By an extension to the dense-fluid regime of a method based upon maximization of entropy subject to constraints, first exploited by Lewis to obtain the Boltzmann equation, kinetic equations for one-particle and two-particle classical distribution functions are obtained. For the hard-sphere potential and a one-particle constraint, the kinetic equation (for the one-particle distribution function) of the revised Enskog theory is obtained; for a two-particle constraint a more general kinetic equation (for the two-particle distribution function) than that studied by Livingston and Curtiss is obtained. For a pair potential with hard-sphere core plus smooth attractive tail, a new mean-field kinetic equation is obtained on the one-particle level. In the Kac-tail limit the equation takes the form of an Enskog-Vlasov equation. The method yields an explicit entropy functional in each case.Explicit demonstration of an H theorem is made for the one-particle theories in a novel way that illustrates the roles of the reversible and irreversible parts of the hard-sphere piece of the collision integral. The latter part leads to the classical form of entropyproduction density as described by linear irreversible thermodynamics and so possesses many of the features of the Boltzmann collision integral. The former part introduces new elements into the entropy-production term. It is noted that the kinetic coefficients of the revised Enskog theory exhibit Onsager reciprocity in the linear regime. Upon consideration of the standard Enskog theory in the linear regime, we construct an entropyproduction density and identify conjugate fluxes and forces and also kinetic coefficients which are shown to exhibit Onsager reciprocity. The standard theory is in disagreement, however, with the results of phenomenological irreversible thermodynamics for the conventional forms of fluxes and forces.

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