  In classical systems, we reexamine how macroscopic structures in equilibrium
state connect with spatial con- straint on the systems: e.g., volume and
density as the constraint for liquids in rigid box, and crystal lattice as the
constraint for crystalline solids. We reveal that in disordered states,
equilibrium macroscopic structure, depend- ing on temperature and on multibody
interactions in the system, is characterized by a single special microscopic
structure independent of temperature and of interactions. The special
microscopic structure depends only on the spatial constraint. We demonstrate
the present findings providing (i) significantly efficient and systematic
prediction of macroscopic structures for possible combination of constituents
in multicomponent systems, and (ii) unique and accurate determination of
multibody interactions in given system from measured macroscopic structure,
without performing trial-and-error simulation.
