Numerical Discrimination of Thermodynamic Monte Carlo Simulations in All Eight Statistical Ensembles

Generalized expressions for thermodynamic propertiesin terms ofensemble averages are discussed for adiabatic and isothermal ensembles.They are implemented in the simulation code ms2 andvalidated by Monte Carlo simulations for the Lennard-Jones fluid.A comparison of the eight statistical ensembles regarding size scalingbehavior, convergence, and stability is provided for state pointsthroughout the homogeneous fluid region. The resulting data are ingood agreement but differ in their statistical distributions. In closedsystems, the statistical quality of the data is better than in opensystems. Overall, the microcanonical ensemble performs best.

Automated summary

Generalized expressions for thermodynamic properties in terms of ensemble averages are discussed for adiabatic and isothermal ensembles. They are implemented in the simulation code ms2 and validated by Monte Carlo simulations for the Lennard-Jones fluid. A comparison of the eight statistical ensembles regarding size scaling behavior, convergence, and stability is provided for state points throughout the homogeneous fluid region. The resulting data are in good agreement but differ in their statistical distributions. In closed systems, the statistical quality of the data is better than in open systems. Overall, the microcanonical ensemble performs best.