Fundamental treatment of molecular-dynamics ensembles

In microcanonical molecular dynamics the conservation of total momentum implies that the trajectories generate an ensemble with constant total momentum. We present the exact statistical mechanics of this microcanonical molecular dynamics ensemble. Using the adiabatic invariant phase volume to define the entropy, exact formulas, containing thermodynamic response functions, are derived for the microcanonical molecular dynamics ensemble and a numerical comparison of these formulas is made with fluctuation formulas which are valid in the thermodynamic limit and often used in molecular dynamics. No significant difference is found between the results calculated using the different formulas for a system of 432 particles; however, for simulations with small numbers of particles or small-cluster studies, the differences could be important.