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Van der Waals equation from the viewpoint of probability distribution and the triple point as the critical point of the liquid-to-solid transition. (English) Zbl 1323.82013
Summary: 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-amorphous-solid transition under negative pressure. The notion of correlation sphere and the two-scale picture on the Hougen-Watson diagram are used.

MSC:
82B26 Phase transitions (general) in equilibrium statistical mechanics
82B27 Critical phenomena in equilibrium statistical mechanics
82D05 Statistical mechanics of gases
82D15 Statistical mechanics of liquids
35Q82 PDEs in connection with statistical mechanics
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