Traditionally, the noequilibrium statistical mechanics is focussed on situations locally close to equilibrium (Green-Kubo formula, Onsager reciproc- ity 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 de- grees of freedom, that is, systems consisting of an infinite number of particles, In an infinite volume and with finite density (thermodynamics) the ordinary Quantum-mechanic description has to be modified.
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