  For classical discrete systems under constant composition, a set of
microscopic state dominantly contributing to thermodynamically equilibrium
structure should depend on temperature and energy through Boltzmann factor,
exp(-bE). Despite this fact, our recent study find a set of special microscopic
state that can characterize equilibrium properties, where these structures can
be know a priori without any thermodynamic information. Here, for binary
system, we extend the theoretical approach to develop a new formulation, where
the special microscopic states at a given, single composition can characterize
equilibrium structure over whole composition. We demonstrate the validity of
the proposed formulation by comparing with results by conventional
thermodynamic simulaton. The results strongly indicate that most information
about composition- and temperature- dependence of thermodynamically equilibrium
structure for disordered state on multiple compositions can be concentrated to
a set of special microscopic state on any single composition.
