  This article aims at revisiting, with the aid of simple and neat numerical
examples, some of the basic features of macroscopic irreversibility, and, thus,
of the mechanical foundation of the second principle of thermodynamics as drawn
by Boltzmann. Emphasis will be put on the fact that, in systems characterized
by a very large number of degrees of freedom, irreversibility is already
manifest at a single-trajectory level for the vast majority of the
far-from-equilibrium initial conditions - a property often referred to as
typicality. We also discuss the importance of the interaction among the
microscopic constituents of the system and the irrelevance of chaos to
irreversibility, showing that the same irreversible behaviours can be observed
both in chaotic and non-chaotic systems.
