Numerical Discrimination of Thermodynamic Monte Carlo Simulations in All Eight Statistical Ensembles
Isabel Nitzke, Jadran Vrabec
Abstract
Generalized expressions for thermodynamic properties in terms of ensemble averages are discussed for adiabatic and isothermal ensembles. They are implemented in the simulation code ms 2 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.
Topics & Concepts
Statistical physicsStatistical ensembleMonte Carlo methodAdiabatic processConvergence (economics)Microcanonical ensembleScalingStability (learning theory)Computer scienceCanonical ensemblePhysicsMathematicsThermodynamicsStatisticsMachine learningEconomicsEconomic growthGeometryPhase Equilibria and ThermodynamicsAdvanced Thermodynamics and Statistical MechanicsStatistical Mechanics and Entropy