2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/17725In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann's analysis, the essence of which I shall review here, is basically correct. The most famous criticisms of Boltzmann's later work on the subject have little merit. Most twentieth century innovations -- such as the identification of the state of a physical system with a probability distribution $\varrho$ on its phase space, of its thermodynamic entropy with the Gibbs entropy of $\varrho$, and the invocation of the notions of ergodicity and mixing for the justification of the foundations of statistical mechanics -- are thoroughly misguided.16 pages, 3 figures. To appear in Chance in Physics: Foundations and Perspectives, edited by Jean Bricmont, Detlef Durr, Maria C. Galavotti, Giancarlo Ghirardi, Francesco Petruccione, and Nino Zanghi, Lecture Notes in Physics 574, (Springer-Verlag)Statistical MechanicsMathematical PhysicsHistory and Philosophy of PhysicsQuantum Physicstext