Non-equilibrium thermodynamics has developed various methods for constructing evolution equations for dissipative processes. In this lecture, I will show, using the examples of Newtonian gravity and Korteweg fluids, that the Second Law of thermodynamics, with correct consideration of Galilean relativistic spacetime and various constraints, determines both the ideal and the dissipative forms of the evolution equations. A general consequence of thermodynamic compatibility is the classical holographic property, i.e. that the volume density can be equivalently written as the divergence of a special constitutive pressure tensor. Further benchmarks are various generalizations of the classical equations, with unexpected physical consequences.
I will show , that quantum mechanics, superfluids, strongly correlated quantum plasmas, and capillary fluids are closely related: it is thermodynamics that links them. I will also briefly discuss various alternative theories of gravity and interpretational issues of quantum mechanics, with particular reference to recent advances in pilot-wave, Bohmian and fluid formulations.