Giovanni Jona-Lasinio

TOWARDS A THERMODYNAMICS OF NONEQUILIBRIUM STATIONARY STATES

Models of stochastic lattice gases have been very popular and very effective in recent years for the study of nonequilibrium steady states using powerful probabilistic techniques. We shall describe how, in spite of the different microscopic features, a unified picture is emerging at the macroscopic level applicable, in principle, to real phenomena where diffusion is the dominating physical mechanism. An interesting feature of the macroscopic level is that one can actually forget the underlying microscopic probabilistic dynamics and develop the theory starting from very general assumptions and using some basic ideas from control theory. Furthermore, since typical nonequilibrium observables like currents involve time in their definition, a space-time thermodynamics emerges naturally. Dynamical phase transitions can appear in which translational invariance in time is spontaneously broken. These lectures will present an overview together with some recent novelties and applications.

The corresponding functionals in the conservative case satisfy a Gallavotti-Cohen type relationship.