  For classical many-body systems, our recent study reveals that expectation
value of internal energy, structure, and free energy can be well characterized
by a single specially-selected microscopic structure. This finding relies on
the fact that configurational density of states (CDOS) for typical classical
system before applying interatomic interaction can be well characterized by
multidimensional gaussian distribution. Although gaussian distribution is an
well-known and widely-used function in diverse fields, it is quantitatively
unclear why the CDOS takes gaussian when system size gets large, even for
projected CDOS onto a single chosen coordination. Here we demonstrate that for
equiatomic binary system, one-dimensional CDOS along coordination of pair
correlation can be reasonably described by gaussian distribution under an
appropriate condition, whose deviation from real CDOS mainly reflects the
existence of triplet closed link consisting of the pair figure considered. The
present result thus significantly makes advance in analytic determination of
the special microscopic states to characterized macroscopic physical property
in equilibrium state.
