Steps toward the foundations of statistical mechanics: in and out of equilibrium

Abstract

The first part of the paper is devoted to the foundations, that is the mathematical and physical justification, of equilibrium statistical mechanics. It is a pedagogical attempt, mostly based on Khinchin’s presentation, which purpose is to clarify some aspects of the development of statistical mechanics. In the second part, we discuss some recent developments that appeared out of equilibrium, such as fluctuation theorem and Jarzynski equality