Abstract: Starting from the Gibbs ensemble theory, the grand canonical distribution function, chemical potential, number fluctuation and energy fluctuation formula of the nearly independent particle system that consists of any number of particles are derived. Based on the hard sphere model, we have performed the computer simulation for the grand canonical distribution function of 2D and 3D mechanic systems. Our results are in agreement with the theory.

Key words: grand canonical ensemble, distribution function, chemical potential, particle number fluctuation, computer simulation