A PROJECTION OPERATOR AND SELF-CONSISTENT-FIELD EQUATIONS FOR REDUCEDNONEQUILIBRIUM DISTRIBUTION-FUNCTIONS

A projection operator is constructed which, when applied to the Liouvi lle equation, yields self-consistent field equations for products of r educed nonequilibrium distribution functions for interacting particles . The self-consistent field equations superficially appear as the evol ution equations for fictitious independent subunits making up the syst em of interest. They, in fact, represent closures of the Bogoliubov-Bo rn-Green-Kirkwood-Yvon hierarchy at various levels of reduced descript ion. When the integral kernel is suitably approximated, they yield the well-known Boltzmann equation and kinetic equations for reduced distr ibution functions for uncorrelated subsystems comprising the system. O n the basis of the self-consistent field equations, some deductions ar e made for kinetic equations that may be used for constructing thermod ynamic theories of irreversible processes consistent with the laws of thermodynamics. (C) 1998 American Institute of Physics. [S0021-9606(98 )51339-6].