Statistical mechanics of stationary states. II. Applications to low-density systems

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Abstract
The singlet distribution function (SDF) and the first two sum rules of the dynamic structure factor in lowdensity simple fluids are computed using the formalism developed in the first paper in this series. It is shown that the correlation-function expression for the SDF reduces to the Chapman-Enskog and Choh-Uhlenbeck forms in the low-density regime. The leading density dependence of the sum rules in nonequilibrium stationary states (NESS), with and without convection is given, and explicit forms for "Maxwell molecules" are computed. The results clearly show that local-equilibrium theories yield incomplete results for the sum rules in the small-wave-vector regime. The fact that time-reversal symmetry is broken in NESS yields the new result that the first sum rule is nonzero even in the absence of convection. Lastly, the validity of the separation of time-scale assumption used in the formal analysis is examined.