Microcanonical thermodynamics of three and four atoms

Clusters are treated in the microcanonical ensemble. Two classical choices for the partition function are used in Boltzmann's assumption for entropy: Phase space volume and phase space density. For both definitions, exact statistical analogs are derived for energy derivatives of entropy to arbitrary order. The analogs are used in rigorous microcanonical Monte Carlo simulation to measure entropy derivatives up to order three for systems of three and four atoms. All simulation results are confirmed by direct numerical integration of the statistical analogs.