Generating functional and the functional analog of Bogolyubov's variational method

On the basis of the generating functional introduced in this work (the functional is a natural generalization of the well-known Bogoliubov's generating functional to the case when path integrals are used in statistical mechanics), the functional analogue of the N. N. Bogoliubov variational method is investigated. The method suggested is illustrated by some nontrivial models of statistical mechanics.