This book presents a critical and modern analysis of the conceptual foundations of statistical mechanics as laid down in Boltzmann's works. The author emphasizes the relation between microscopic reversibility and macroscopic irreversibility. Students will find a clear and detailed explanation of fundamental concepts such as equipartition, entropy, and ergodicity. They will learn about Brownian motion, the modern treatment of the thermodynamic limit phase transitions, the microscopic and macroscopic theory of the coexistence of phases, statistical mechanics of stationary states, and fluctuations and dissipation in chaotic motions.

The author is one of the leading scientists in mathematical physics and a well-known expert in statistical mechanics This work on the fundamental concepts is unparalleled in the literature Includes supplementary material: sn.pub/extras

Autorentext

Giovanni Gallavotti, emeritus, has been fellow at IHES (Paris, 1966-1968) with David Ruelle and post doc at Rockefeller University (New York, 1968-1970) with Mark Kac. He has been, since 1972, full professor in various universities (Napoli, Roma2 and Roma1). He has been long term visitor at IHES, IAS, Nijmegen, Princeton and Rutgers University. His primary research focused subsequently on theoretical and historical aspects of Equilibrium Statistical Mechanics, Quantum field theory, Low temperature Fermi systems, Nonequilibrium and, currently, concentrates on mathematical problems on Fluid mechanics. Recipient of several awards and prizes (Presidente della Repubblica prize, Boltzmann medal, Henri Poincare' prize).

Inhalt

1. Classical Statistical Mechanics.- 2. Statistical Ensembles.- 3. Equipartition and Critique.- 4. Thermodynamic Limit and Stability.- 5. Phase Transitions.- 6. Coexistence of Phases.- 7. Exactly Soluble Models.- 8. Brownian Motion.- 9. Coarse Graining and Nonequilibrium.- Name Index.