  The thermodynamic limit in statistical thermodynamics of many-particle
systems is an important but often overlooked issue in the various applied
studies of condensed matter physics. To settle this issue, we review tersely
the past and present disposition of thermodynamic limiting procedure in the
structure of the contemporary statistical mechanics and our current
understanding of this problem. We pick out the ingenious approach by N. N.
Bogoliubov, who developed a general formalism for establishing of the limiting
distribution functions in the form of formal series in powers of the density.
In that study he outlined the method of justification of the thermodynamic
limit when he derived the generalized Boltzmann equations. To enrich and to
weave our discussion, we take this opportunity to give a brief survey of the
closely related problems, such as the equipartition of energy and the
equivalence and nonequivalence of statistical ensembles. The validity of the
equipartition of energy permits one to decide what are the boundaries of
applicability of statistical mechanics. The major aim of this work is to
provide a better qualitative understanding of the physical significance of the
thermodynamic limit in modern statistical physics of the infinite and "small"
many-particle systems.
