  Our recent study elucidate that information of density of states in
configuration space (CDOS) for non-interacting system, characterized by spatial
constraint on the system, plays essential role to determine thermodynamically
equilibrium properties for interacting systems. Particularly for disordered
states, variance of CDOS along all possible coordinations plays significant
role. Despite this fact, even for binary system of crystalline solids, analytic
expression for variance of CDOS as a function of composition has not been
clarified so far. Here we successfully derive variance of CDOS as a function of
composition for pair correlations, whose validity is demonstrated by comparing
the results with uniform sampling of CDOS on real lattices. The present result
certainly advances determining special microscopic state to characterize
Helmholtz free energy in classical systems, whose structure is difficult to
determine by numerical simulation.
