  Expectation value of dynamical variables in thermodynamically equilibrium
state can be typically provided through well-known canonical average. The
average includes tremendous number of possible states considered far beyond
practically handled, which makes it difficult to obtain analytic representation
of the average to clarify how the expectation value connects with given
interaction: i.e., the relationship is generally understood in phonomenological
manner except for modest, simple models. Here we show that the relationship is
explicitly clarified for discrete large systems, where the configurational
density of states for any single pair correlation is represented in terms of
linear combination of Dirac delta function and its derivatives. The significant
advantage of the present representation is that it can decompose contributions
to macroscopic dynamical variables into harmonicity and anharmonicity in terms
of their underlying structural degree of freedom, which will lead to find a set
of special microscopic state to characterize macroscopic properties in
equilibrium state for classical many-body systems.
