  The aim of this review is to provide better understanding of a few approaches
that have been proposed for treating nonequilibrium (time-dependent) processes
in statistical mechanics with the emphasis on the inter-relation between
theories. The ensemble method, as it was formulated by J. W. Gibbs, have the
great generality and the broad applicability to equilibrium statistical
mechanics. Different macroscopic environmental constraints lead to different
types of ensembles, with particular statistical characteristics. In the present
work, the statistical theory of nonequilibrium processes which is based on
nonequilibrium ensemble formalism is discussed. The kinetic approach to dynamic
many-body problems, which is important from the point of view of the
fundamental theory of irreversibility, is alluded to. The emphasis is on the
method of the nonequilibrium statistical operator (NSO) developed by D. N.
Zubarev. The NSO method permits one to generalize the Gibbs ensemble method to
the nonequilibrium case and to construct a nonequilibrium statistical operator
which enables one to obtain the transport equations and calculate the transport
coefficients in terms of correlation functions, and which, in the case of
equilibrium, goes over to the Gibbs distribution. Although some space is
devoted to the formal structure of the NSO method, the emphasis is on its
utility. Applications to specific problems such as the generalized transport
and kinetic equations, and a few examples of the relaxation and dissipative
processes, which manifest the operational ability of the method, are
considered.
