Non-Equilibrium Statistical Mechanics

Abstract

In the preceding chapter we discussed the microscopic foundations of extended irreversible thermodynamics through fluctuation theory. The present chapter deals with more general methods of non-equilibrium statistical mechanics. First, we start from the Liouville equation and introduce the projection operator technique to relate the memory function to the time correlation function of the fluctuations of the fluxes, a key result in modern non-equilibrium statistical mechanics. This result is of special interest in EIT, because it emphasizes the role played by the evolution of the fluctuations of the thermodynamic fluxes. Furthermore, the method of projection operators is useful, since it provides an explicit method for formulating the dynamical equations of the basic variables. Classically, the set of variables consists of the conserved slow variables (energy, linear momentum, mass) and some order parameters characterizing second-order phase transitions. Here we shall present a generalization of this method by adding the dissipative fast fluxes to the basic set of variables.