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Resolution of the hierarchy of many-body distribution functions

The rigorous evolution equation for the one-body distribution function f(t) describing an imperfect gas is not closed according to the investigations of Bogoliubov, Born, Green, Kirkwood, Yvon and others (B—B—G—K-Y hierarchy). The analysis of this equation is made in terms of connected diagrams. It is shown that in the bulk limit this equation can rigorously be transformed into an equation which is closed with respect to f(t) and which contains a given initial correlation. The latter equation forms a basis of discussing various problems related to irreversibility and transport phenomena.