From BBGKY Hierarchy to Non-Markovian Evolution Equations

The problem of description of the evolution of the microscopic phase density and its generalizations is discussed. With this purpose, the sequence of marginal microscopic phase densities is introduced, and the appropriate BBGKY hierarchy for these microscopic distributions and their average values is formulated. The microscopic derivation of the generalized evolution equation for average value of the microscopic phase density is given and the non-Markovian generalization of the Fokker-Planck collision integral is deduced.