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In the present paper the gas, liquid and solid phases made of structurelessparticles, are visited to the light of the quantum stochastic hydrodynamicanalogy (SQHA). The SQHA shows that the open quantum mechanical behavior ismaintained on a distance shorter than the theory-defined quantum correlationlength (lc). When, the physical length of the problem is larger than lc, themodel shows that the quantum (potential) interactions may have a finite rangeof interaction maintaining the non-local behavior on a finite distance quantumnon-locality length lq. The present work shows that when the mean moleculardistance is larger than the quantum non-locality length we have a classicalphases (gas and van der Waals liquids) while when the mean molecular distancebecomes smaller than lq or than lc we have phases such as the solid crystal orthe superfluid one, respectively, that show quantum characteristics. The modelagrees with Lindemann empirical law (and explains it), for the mean squaredeviation of atom from the equilibrium position at melting point of crystal,and shows a connection between the maximum density at the He lambda point andthat one near the water-ice solidification point.

Open Quantum to classical phases transition in the stochastic  hydrodynamic analogy: the explanation of the Lindemann relation and the  analogies between the maximum of density at He lambda point and that one at  water-ice phase transition