Landscape of Configurational Density of States for Discrete Systems at Equicomposition

Abstract

  For classical, discrete many-body systems in thermodynamically equilibrium state, expectation value of internal energy, structure, and free energy can be well characterized by a single specially-selected microscopic structure, which is recently revealed by our study. This finding relies on the fact that configurational density of states (CDOS) for typical classical system under constant composition before applying interatomic interaction can be well characterized by multidimensional gaussian distribution. Although gaussian distribution is an well-known and widely-used function in diverse fields, it is quantitatively unclear why the CDOS takes gaussian when system size gets large, even for projected CDOS onto a single chosen coordination. Here we demonstrate that for binary system at equicomposition, one-dimensional CDOS along coordination of pair correlation can be reasonably described by gaussian distribution under an appropriate condition, whose deviation from real CDOS mainly reflects the existence of triplet closed link consisting of the pair figure considered. The present result will make significant advances in analytic determination of the special microscopic states to characterized macroscopic physical property in equilibrium state.