Van der Waals Equation from the Viewpoint of Probability Distribution and the Triple Point as the Critical Point of the Liquid-to-Solid Transition

We show that a distribution of the type of the Bose-Einstein distribution describes the van der Waals gas, while the Fermi-Dirac distribution describes the van der Waals liquid. We present the construction of the binodal, the melting curve, and the liquid-to-amorphoussolid transition under negative pressure. The notion of correlation sphere and the two-scale picture on the Hougen-Watson diagram are used.