Configurational density of states of finite classical systems

TL;DR

This paper introduces an explicit inversion formula to compute the configurational density of states (CDOS) from the total density of states (DOS) in finite classical systems, simplifying thermodynamic analysis.

Contribution

It provides a novel microcanonical framework that avoids Laplace transform inversion for calculating CDOS from DOS in finite systems.

Findings

Derives an explicit formula for CDOS from DOS

Recovers asymptotic thermodynamic results for large systems

Facilitates thermodynamic analysis of small classical systems

Abstract

The configurational density of states (CDOS) encodes all the relevant thermodynamic information contained in the interaction potentials for statistical mechanical systems. However, its explicit computation is usually a challenge for non-trivial systems, and numerical algorithms such as Wang-Landau simulation are often used. In this work we use a microcanonical framework to provide an explicit inversion formula for the calculation of the CDOS from the total density of states (DOS) without resorting to the inversion of the Laplace transform. From this formula, several results can be obtained for the thermodynamics of finite classical systems composed of a few degrees of freedom, while also recovering the well-known asymptotic results for the thermodynamic limit.