Microcanonical Monte Carlo simulation of thermodynamic properties

A rigorous sampling procedure in configurational phase space is used to simulate any thermodynamic property in the microcanonical ensemble. It is shown how two classical choices of W in Boltzmann’s ${\mathrm{S=k}}_B\hspace{0.17em}\ln \mathrm{\hspace{0.17em}W}$ differ for small systems and become numerically equivalent in the thermodynamic limit. The same holds true for the comparison with classical molecular dynamics simulations. A comparison with the best empirical equations of state for the Lennard-Jones system shows that this Monte Carlo method is as accurate and reliable as any other simulation technique.