Equivalence of two forms of the nonequilibrium statistical operator

The equivalence of two variants of the nonequilibrium statistical operator method is proved: NSO-1 (canonical distribution of quasi-integrals of the motion) and NSO-2 (invariant part of the quasi-equilibrium distribution). It is shown that in the general case every solution of the NSO-2 balance equations is a solution of the NSO-1 balance equations. The proof is based on convexity inequalities and does not contain any assumptions of physical nature going beyond the original formulation of the nonequilibrium statistical operator method.