Journal of Statistical Physics, Vol. 24, No. 2, 1981, p. 301-324.
A new theoretical description of nonequilibrium phenomena has been obtained that is analogous to the very successful Percus-Yevick equation of equilibrium fluids. The success of the equilibrium Percus-Yevick theory in describing hard-core systems suggests the nonequilibrium analog will also be quite good. Previously, we reported a new construction of the equilibrium Percus-Yevick equation which is applicable in the nonequilibrium domain and utilizes the BBGKY hierarchy in addition to some elementary ideas of functional expansions. The nonequilibrium Percus-Yevick theory contains an appealing physical picture wherein two fluid particles interact via an effective interaction Liouville operator which is the "true" interaction Liouville operator weighted by the (renormalized) second correlation function. The Percus-Yevick analog equation includes the usual "simple ring" and "repeated ring" dynamical processes in addition to more unusual "ring within ring" processes. The equilibrium Percus-Yeviek theory indicates these "ring within ring" processes should be quantitatively important especially for dense gases and liquids.