Abstract:
The fundamental idea by N. N. Bogoliubov about reducing the description of equilibrium
statistical systems is applied to the problem of deriving the equation for the
radial disrtibution function (RDF) of particles in simple classical liquids. A projective
construction of the reduced description of equilibrium state is developed which is based
on Bogoliubov's idea about the successive taking into account the nierarchy of interactions
in many-particle systems. Generalised integro-differential equation for the
RDF is obtained which after partial linearization and different simplifications leads to
the well-known equations by Bogoliubov, Kirkwood–Salzburg, Percus–Yevick, superintertwining
chains, etc. New additional contributions due to correlations between
particles are found in the linear and quadratic (with respect to the density) terms in
the equation.
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