Configurational density of states of finite 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.