Contemporary methods of the statistical theory of nonequilibrium processes

Possible approaches to the construction of nonequilibrium equations from first principles are analyzed: the prescription of the initial state at time $t=0$ and the investigation of the asymptotics as $t\to\infty$ as well as methods of averaging over the initial times or boundary conditions in the distant past. In simple examples, a comparison is made of the methods of the projection operator and the nonequilibrium statistical operator (in two versions) of Kubo–Yokota–Nakajima, Mori, Robertson, Kawasaki–Gunton, Kadanoff–Martin, etc.