Quantative measure of efficiency of Monte Carlo simulations

An easily applied, physically motivated algorithm for determining the efficiency of Monte Carlo simulations is introduced. The theoretical basis for the algorithm is developed. As an illustration we apply the method to the Lennard-Jones liquid near the triple point. We show that an acceptance ratio of 0.2 is twice as efficient for the purpose of generating a satisfactory sample as is an acceptance ratio of 0.5. There is a strong correlation between the efficiency measure and the diffusion rate of liquid particles during the simulation. We argue that the optimal value of the acceptance ratio is calculable from short Monte Carlo simulations. The method is very general and is applicable to Monte Carlo simulations involving arbitrary potentials.