On the Grand Canonical Distribution Method of Statistical Mechanics

Usually, the grand canonical distribution method is derived only through plausibility arguments, and up to the present its accurate proof has never been basing directly on ergodic theorem. In order to give the method a sound basis, we attempt to reformulate this in the case of ordinary classical liquids, and show that it is practically equivalent to both the microcanonical and the canonical distribution methods. As the result, we can safely use any one of the three methods of statistical mechanics, even for the purpose of investigating phase change.