Nonequilibrium Statistical Mechanics

Abstract.

 Traditionally, the nonequilibrium statistical mechanics is focussed on situations locally close to equilibrium (Green-Kubo formula, Onsager reciprocity relations) or to return to equilibrium (Boltzmann). In these lecture we will be concerned with nonequilibrium statistical mechanics far from equilibrium. After a brief survey of the classical case, we will focus our attention to the quantum case. For quantum systems with an infinite number of occupied degrees of freedom, that is, systems consisting of an infinite number of particles, in an infinite volume and with finite density (thermodynamics) the ordinary quantum-mechanics description has to be modified. This lead us to work in an algebraic framework well suited for the investigation of such systems. We will discuss the basic ideas of algebraic approach: observables, time evolution, local perturbation, cyclic representation, Liouvillean, and particularly nonequilibrium steady states.