Hypervolumes in microcanonical Monte Carlo Original Research Article

A Monte Carlo method to perform microcanonical simulations by sampling the configurational and momenta spaces is presented. The technique was inspired by the method of hypervolumes for calculating the entropy in a microcanonical ensemble. Although this method is strictly proven in the thermodynamic limit, the hypervolume Monte Carlo (HVMC) algorithm, presented in this article, works well with a relatively small number of particles. In contrast to other algorithms for microcanonical Monte Carlo simulations, the HVMC method does not involve previous integrations over the momenta space or demons. Therefore, it can be used with any form of Hamiltonian. Thermal and structural properties for the Lennard-Jones system obtained by NVE molecular dynamics are compared with results from the HVMC method. The agreement is excellent. Additionally, the method provides the speed distribution functions of the system which are, also, in excellent agreement with the results from molecular dynamics. A discussion of the HVMC method in the context of the statistical mechanical theory of the microcanonical ensemble is presented.