# Landscape of Configurational Density of States for Discrete Large Systems

## TL;DR

This paper demonstrates that the configurational density of states (CDOS) in large classical many-body systems can be approximated by a Gaussian distribution, advancing the understanding of microscopic states in equilibrium.

## Contribution

It provides an analytic explanation for the Gaussian nature of CDOS in large systems and relates deviations to triplet interactions, improving microscopic state characterization.

## Key findings

- CDOS approximates a Gaussian distribution in large systems
- Deviation from Gaussian linked to triplet interactions
- Advances in analytic determination of microscopic states

## Abstract

For classical many-body systems, our recent study reveals that expectation value of internal energy, structure, and free energy can be well characterized by a single specially-selected microscopic structure. This finding relies on the fact that configurational density of states (CDOS) for typical classical system 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 equiatomic binary system, 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 thus significantly makes advance in analytic determination of the special microscopic states to characterized macroscopic physical property in equilibrium state.