Foundations and applications of non-equilibrium statistical mechanics

For systems that are in equilibrium with their environment, the knowledge of a small set of parameters characterizing it (temperature, pressure, etc) is sufficient to fully specify the statistical and thermodynamic properties of the system. Under out-of-equilibrium conditions, a description of such generality is not available, basically because the system state depends on the coupling with the environment (e.g. the heath baths), and on the details of the system dynamics. As a consequence, there is no straightforward generalization of the equilibrium thermodynamical potentials describing the state probability distribution of a system out of equilibrium, nor a conclusive understanding of how non-equilibrium phenomena emerge out of the underlying microscopic dynamics.