Campisi, Michele. creator author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text sz 2024 2nd ed. 2024. monographic eng

electronic

electronic resource

access XV, 114 p. 22 illus., 17 illus. in color. online resource. This book provides a modern pedagogical exposition of the mechanical approach to statistical mechanics initiated by Boltzmann with his early works (1866–1871). Despite the later contribution by Helmholtz, Boltzmann himself (1884–1887), Gibbs, P. Hertz, and Einstein, the mechanical approach remained almost unknown to the modern reader, in favour of the celebrated combinatorial approach, developed by Boltzmann himself during his probabilistic turn (1876–1884). The brief constitutes an ideal continuation of a graduate course of classical mechanics and requires knowledge of basic calculus in many dimensions (including differential forms), thermodynamics, and probability theory, besides Hamiltonian mechanics. The cornerstone of the whole presentation is the ergodic hypothesis. Special attention is devoted to Massieu potentials (the Legendre transforms of the entropy) which are most natural in statistical mechanics and also allow for a more direct treatment of the topic of ensemble equivalence. In this second edition, a chapter is added that addresses the long-debated question of how the second law of thermodynamics can be reconciled with mechanics, by taking advantage of modern methods of non-equilibrium statistical mechanics. 1. The Constitutive Statements of Thermodynamics -- 2. Minimal Mechanical Model of Thermodynamics -- 3. The Microcanonical Ensemble -- 4. The Canonical Ensemble -- 5. The TP Ensemble -- 6. The Grandcanonical Ensemble -- 7. Ensemble (in)-Equivalence -- 8. Statistical mechanical foundation of the law of entropy increase. by Michele Campisi. Thermodynamics Statistical Physics Mathematical physics Thermodynamics Statistical Physics Mathematical Methods in Physics QC310.15-319 9783031570452 https://doi.org/10.1007/978-3-031-57045-2 https://doi.org/10.1007/978-3-031-57045-2 250121 20251030114928.0 978-3-031-57045-2