Configurational density of states of finite classical systems

In this work, using a microcanonical framework, we provide an explicit inversion formula that allows the calculation of the configurational density of states from the total density of states without resorting to the inversion of the Laplace transform. From this formula, several results can be obtained for the thermodynamics of classical systems composed of a few degrees of freedom, while at the same time recovering the well-known behavior in the thermodynamic limit.