This book — the third in a set, following two standalone companions that introduce standard techniques of statistical mechanics – is a new edition of Problems on Statistical Mechanics (D. A. R. Dalvit et al, 1999, CRC Press).
A thorough understanding of statistical mechanics depends strongly on the insights and manipulative skills that are acquired through the solving of problems. This book provides 268 problems with model solutions, illustrating both basic principles and applications.
The problems occupy fourteen chapters, progressing from the simpler aspects of thermodynamics and equilibrium statistical ensembles to the more challenging ideas associated with strongly interacting systems and nonequilibrium processes.
Each chapter consists of exercises spanning multiple levels of difficulty, from warm-up derivations to longer problems that connect several ideas. The solutions are written to be instructive rather than minimal and, in several places, include short contextual remarks - why a technique matters, what it is used for elsewhere, and how it relates to alternative approaches.
The exercises are based on the content of the first two volumes of this set:
- F. Caravelli and D. A. R. Dalvit, Practical Statistical Mechanics: Thermodynamics and Statistical Mechanics, Volume 1, CRC Press (2026).
- F. Caravelli, J. Zanella Béguelin, and D. A. R. Dalvit, Practical Statistical Mechanics: Advanced Statistical Mechanics, Volume 2, CRC Press (2027).
Key Features:
- Contains over 600 pages of worked problems in statistical mechanics and thermodynamics
- Comprehensive solutions to all problems are designed to illustrate efficient and elegant problem-solving techniques
- Serves as a reliable companion to studying the topic: something to consult when you are stuck, to compare approaches, and to learn what a complete solution looks like in this subject
Table of Contents:
1. Introduction 2. Thermodynamics 3. Classical Ensembles: Discrete States 4. Classical Ensembles: Continuous States 5. Quantum Ensembles 6. Bose and Fermi Gases 7. Classical Many-Body Systems 8. Phase Transitions and Renormalization Group 9. Frustration and Disorder 10. Monte Carlo 11. Information Theory and Statistical Mechanics 12. Stochastic Processes and Non-Equilibrium Thermodynamics 13. Quantum Many-Body Systems 14. Machine Learning and Inference 15. Appendix: Useful Formulae
About the Author :
Francesco Caravelli is a physicist whose research spans equilibrium and non-equilibrium statistical mechanics, dynamical and complex systems, and quantum technologies. He began his scientific career in quantum gravity at the University of Waterloo and the Perimeter Institute, later moving into complex systems during positions at the University of Oxford and University College London, followed by research in the private sector. Since joining Los Alamos National Laboratory in 2017, first as an Oppenheimer Fellow and later as a Staff Scientist in T4, he has investigated the dynamics of memristive and neuromorphic circuits, deriving exact results that link their memory properties to foundational principles of statistical physics. His recent work focuses on collective nonlinear dynamics, neuromorphic computing, low-power analog architectures, and emerging directions in quantum computing.
Juan Zanella Béguelin received his B.Sc. in Physics from Instituto Balseiro and his Ph.D. from the University of Buenos Aires, where he currently teaches theoretical physics. He has ample expertise in solved problems on thermodynamics and statistical mechanics.
Alioscia Hamma is a theoretical physicist and associate professor at the University Federico II of Naples. Specializing in quantum information theory, his research spans quantum algorithms, foundations of quantum mechanics, black hole physics, quantum chaos, and complexity. After earning his PhD in Naples, he held positions at USC, MIT, Perimeter Institute, Tsinghua, and UMass Boston.
Diego A. R. Dalvit is a Senior Staff Member at the Theoretical Division of Los Alamos National Laboratory. He is a quantum optics theorist with expertise in Casimir physics, statistical mechanics, quantum sensing, and metamaterials. He received his Ph.D. in Physics from Universidad de Buenos Aires (Argentina) in 1998. He is a Fellow of the American Physical Society and Optica. He has authored more than 110 peer-reviewed papers, with more than 10,000 citations. He has also co- authored two physics textbooks, one a guide to the essence of Casimir physics, and one on problems on statistical mechanics.
