Boltzmann, Ratchets and Avalanches

摘要

The title of this course may lead to the impression that it deals with three disconnected topics of the general field of statistical physics. Namely, the use of Boltzmann equation to describe the relaxation to equilibrium of a simple gas; the understanding of the appearance of currents in so-called forced thermal ratchets, via the Langevin equation; and the description of avalanches in granular materials, employing the techniques associated with the Master equation. In a way these are indeed different physical problems and separate subfields of research. However, as these lectures will show, we can associate these three subjects with one another because they all deal with systems where internal noise plays a fundamental role. They are also joined through the theoretical tools that have been devised to deal with them.' At a deeper level, the thread that weaves through those themes is the understanding and application of the Second Law of Thermodynamics to many-body systems, either in a closed environment or in contact with an external field.