Lecture - online event

Abstract: The quasi-static scaling limit corresponds to changes of the boundary conditions (boundary tension, temperature heat bath, density of particle reservoirs) on a time scale that is slower (i.e. larger) than the equilibrium relaxation scale of the dynamics in the bulk. In this very large time scale, the system is always very close to the global stationary state corresponding to the (time varying) tension, temperatures or densities applied at the boundaries. These quasi-static evolutions are usually presented as idealization of real thermodynamic transformations. On the other hand they are necessary concepts in order to construct thermodynamic potentials, for example to define thermodynamic entropy from Carnot cycles. The existence of the quasi-static transformations can be seen as another thermodynamic principle that needs to be derived from the microscopic dynamics under a proper space-time scaling that we call quasi-static hydrodynamic limit. We are particularly interested in studying quasi-static transformations among non-equilibrium stationary states (NESS). I will expose some results concerning quasi-static hydrodynamic limits for dynamics with diffusive behavior (like symmetric simple exclusion and anharmonic chains in contact with heat bath in the bulk and tension at the boundary) and hyperbolic/ballistic behavior (like the asymmetric simple exclusion). We also studies the large deviations from these quasi-static limits and the relation with the large deviations in the corresponding NESS. Works in collaboration with Anna de Masi, Lu Xu, Stefano Marchesani .