This book provides a modern pedagogical exposition of the mechanical approach to statistical mechanics initiated by Boltzmann with his early works (18661871). Despite the later contribution by Helmholtz, Boltzmann himself (18841887), 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 (18761884). 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 using modern methods of non-equilibrium statistical mechanics.

Introduces a new chapter discussing the increase of entropy in non-equilibrium Presents the forgotten mechanical approach of Boltzmann in a pedagogical, original, and organic manner Includes supplements and exercises covering topics of recent research

Autorentext

Dr. Michele Campisi is a tenured researcher at the Institute for Nanoscience of Italy's National Research Council (CNR) and Lecturer in Quantum Thermodynamics at the University of Pisa, Italy. He earned his Ph.D. in Physics in 2008 from the University of North Texas, USA, for which he received the Robert S. Hyer Recognition for Excellence in Research, along with his supervisor, Prof. Don H. Kobe. He has been a research fellow at the University of Augsburg, Germany, where he pursued an intense research programme on non-equilibrium thermodynamics of quantum systems with Prof. P. Hanggi and Prof. P. Talkner. In 2014, he was awarded a Marie Curie Intra-European Fellowship with a project on Non-equilibrium thermodynamic fluctuations in superconducting devices, which he pursued at Scuola Normale Superiore, Pisa, Italy. He then joined the faculty of the University of Florence, Italy, where he taught the course of Statistical Mechanics.

Inhalt

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.