Grand Projection State: A Single Microscopic State to Determine Free Energy

Abstract

In classical systems, we recently clarified the relationship between the spatial constraint and equilibrium macroscopic properties (especially, dynamical variables) in disordered states under a canonical ensemble: We found that a few special microscopic states, whose structures can be constructed without any information about the energy or temperature, can describe macroscopic properties. In this study, we extend our approach to a grand canonical ensemble, which finds a single special microscopic state to determine not only a grand-canonical average of the composition but also the Helmholtz free energy in a binary system, which has not been described by a single state.