  We consider hydrodynamic limits of interacting particles systems with open
boundaries, where the exterior parameters change in a time scale slower than
the typical relaxation time scale. The limit deterministic profiles evolve
quasi-statically. These limits define rigorously the thermodynamic quasi static
transformations also for transition between non-equilibrium stationary states.
We study first the case of the symmetric simple exclusion, where duality can be
used, and then we use relative entropy methods to extend to other models like
zero range systems. Finally we consider a chain of anharmonic oscillators in
contact with a thermal Langevin bath with a temperature gradient and a slowly
varying tension applied to one end.
