Nonequilibrium Phenomena: I. Kinetic Methods

Abstract

In the previous chapters of this book we have always referred to phenomena in macroscopic equilibrium, which can be treated and well understood by the formalism of Gibbs ensembles. In this chapter, we revisit the old problems of Ludwig Boltzmann, who directed most of his efforts to the investigation of the time evolution of systems toward equilibrium. Using a kinetic method, we initially derive the famous Boltzmann equation for a diluted fluid, which still remains an important theoretical technique to deal with transport problems. We then prove the H-theorem, which comes from the Boltzmann equation and provides a description of the route to equilibrium. The historical debates about the meaning of the H-theorem, including objections and answers by Boltzmann, very much up to date, contributed a great deal to clarify the character of statistical physics.