Second order phase transitions describe in a macroscopic manner the decay of energy of a physical system Applied to fluid turbulence, they lead to a proof of existence of non-smooth solutions for the Navier-Stokes equation, with the mathematical proof outlined here. Applied to Yang-Mills quantum fields, they give rise to the mass gap, a Millenium Prize problem. Applied to cosmology and astrophysics, they support a novel explanation for dark matter and dark energy.