Generating Functionals in Nonequilibrium Statistical Mechanics

The main ideas and methods of calculations within the framework of the generating functional technique are considered in a systematical way. The nonequilibrium generating functionals are defined as functional mappings of the nonequilibrium statistical operator and so appear to be dependent on a certain set of macroscopic variables describing the nonequilibrium state of the system. The boundary conditions and the differential equation of motion for the generating functionals are considered which result in an explicit expression for the nonequilibrium generating functionals in terms of the so‐called coarse‐grained generating functional being the functional mapping of the quasiequilibrium statistical operator. Various types of integral equations are derived for the generating functionals which are convenient to develop the perturbation theories with respect to either small interaction or small density of particles. The master equation for the coarse‐grained generating functionals is obtained and its connection with the generalized kinetic equations for a set of macrovariables is shown. The derivation of the generalized kinetic equations for some physical systems (classical and quantum systems of interacting particles, the Kondo system) is treated in detail, with due regard for the polarization effects as well as the energy and momentum exchange between the colliding particles and the surrounding media.