Practical Statistical Mechanics

This book — the first of two companion volumes, together with a third dedicated entirely to exercises — is devoted to introducing the standard techniques of statistical mechanics; presenting a practical, operative, and attentive approach to the recurring structures that link different areas of statistical physics.

It strikes a balance between breadth and an accessible walk-through approach to calculations and concepts that students and researchers will encounter across the many corners of modern statistical mechanics. It is a broad, accessible starting point enabling readers to then move on to more focused and advanced treatments. It also touches on topics that have become increasingly relevant in recent years, including applications of machine learning to elements of quantum information and computing.

Chapters include short experimental boxes that connect theoretical concepts with laboratory demonstrations—from critical phenomena in fluids and magnets to frustrated spin systems. To support learning by doing, it also provides simple numerical codes that illustrate several topics throughout the text.

This will serve as an ideal textbook for undergraduate and graduate courses on Statistical Mechanics and Thermodynamics. It can also be used as supplementary reading for courses on Many-Body Physics.

Key features:

• A one-stop compendium of major results of standard and modern Statistical Mechanics

• Includes pedagogical boxes containing worked examples, historical perspectives, suggested further activities and experimental notes and connections to real world systems.

• Each chapter is structured to serve as a two-hour lecture on the topic, with accompanying calculations

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.

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 9,800 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.