  For classical system under constant composition, macroscopic structure in
thermodynamically equilibrium state can be determined through the so-called
canonical average, including sum over possible microscopic states on phase
space. Although a set of microscopic structure dominantly contributing to
equilibrium properties should depend on temperature and many-body interactions,
we recently clarify that at high temperature, they are universally
characterized by a single special microscopic state (which we call projection
state: PS), whose structure can be known a priori without any thermodynamic
information. Here we extend this approach to find additional special
microscopic states, enabling us to characterize equilibrium structures for
lower-temperature region above transition temperature. The concept of our
approach will lead to a new paradigm; the formulation of macroscopic properties
by special microscopic states basis.
