  Recently Mazenko and Das and Mazenko introduced a non-equilibrium field
theoretical approach to describe the statistical properties of a classical
particle ensemble starting from the microscopic equations of motion of each
individual particle. We use this theory to investigate the transition from
those microscopic degrees of freedom to the evolution equations of the
macroscopic observables of the ensemble. For the free theory, we recover the
continuity and Jeans equations of a collisionless gas. For a theory containing
two-particle interactions in a canonical perturbation series, we find the
macroscopic evolution equations to be described by the
Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy (BBGKY hierarchy) with a
truncation criterion depending on the order in perturbation theory. This
establishes a direct link between the classical and the field-theoretical
approaches to kinetic theory that might serve as a starting point to
investigate kinetic theory beyond the classical limits.
