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Structure of Non-Solid Matter in Equilibrium State under NVT ensemble: New Insight from Spatial Constraint

When non-solid matter (e.g., liquids or gas) is under constant volume V and density rho (e.g., in rigid box), spatial positions for their constituents are restricted by these conditions. We recently focus on the role of constraint in classical statistical thermodynamics, and find how spatial constraint connects with equilibrium properties for crystalline solids, which has not been clarified so far. The present study extend the idea to non-solid matter under NVT ensemble in classical systems. We provide explicit representation of canonical average of radial distribution function in terms of spatial constraint, which can be well characterized by a single special microscopic state on configuration space called projection state for non-solid matter. We demonstrate that the special microscopic state can be numerically constructed for a finite number of particles.