Problems with the formulation of Relativistic Astrophysics lead to the need for a variational formulation of thermodynamics. This is easy and immensely rewarding in the non relativistic context, so long as the motion is irrotational. The main topic of this talk is to overcome this limitation. The solution is amazingly simple; one has to combine two familiar forms of hydrodynamics. but it is shocking and even revolutionary nevertheless. Some basic tenets have to be given up, with interesting consequences. The application to General Relativity will be sketched at the end.