Statistical Physics and Thermodynamics: An Introduction to Key Concepts

Statistical physics and thermodynamics describe the behaviour of systems on the macroscopic scale. Their methods are applicable to a wide range of phenomena: from refrigerators to the interior of stars, from chemical reactions to magnetism. Indeed, of all physical laws, the laws of thermodynamics are perhaps the most universal. This text provides a concise yet thorough introduction to the key concepts which underlie statistical physics and thermodynamics. It begins with a review of classical probability theory and quantum theory, as well as a careful discussion of the notions of information and entropy, prior to embarking on the development of statistical physics proper. The crucial steps leading from the microscopic to the macroscopic domain are rendered transparent. In particular, the laws of thermodynamics are shown to emerge as natural consequences of the statistical framework. While the emphasis is on clarifying the basic concepts, the text also contains many applications and classroom-tested exercises, covering all major topics of a standard course on statistical physics and thermodynamics.

Table of Contents:
1: Introduction 1.1: The Challenge of Statistical Mechanics 1.2: Classical Probability 2: Quantum Theory 2.1: Review of Basic Concepts 2.2: Mixed States 2.3: Composite Systems 3: Constructing the State 3.1: Information and Entropy 3.2: Maximum Entropy Principle 3.3: Thermodynamic Square 3.4: Reproducible Processes and the Second Law 3.5: Equilibrium and Temperature 3.6: Fluctuations 4: Simple Systems 4.1: Harmonic Oscillator 4.2: Rotor 4.3: Spin in a Magnetic Field 4.4: Paramagnet 5: Thermodynamic Limit 5.1: Homogeneity 5.2: Stability 5.3: Equivalence of Ensembles 5.4: Four Laws 6: Perfect Gas 6.1: Generic Properties 6.2: Continuum and Classical Limits 6.3: Fermi Gas 6.4: Bose--Einstein Condensation 6.5: Photons 6.6: Internal Dynamics 6.7: Dilute Solution 7: Processes and Responses 7.1: Work and Heat 7.2: Cycles, Barriers, and Reservoirs 7.3: Potentials 7.4: Equilibrium and Stability in the Presence of a Reservoir 7.5: Coefficients 8: Phase Transitions 8.1: Coexistence of Phases 8.2: First-Order Phase Transition 8.3: Second-Order Phase Transition: Ising Model

About the Author :
Jochen Rau received degrees in physics and mathematics from Goethe University Frankfurt, University of Cambridge, and Duke University. He has taught theoretical physics at Goethe University Frankfurt and Ulm University, Germany, and is currently Professor of Mathematics at RheinMain University of Applied Sciences, Germany.

Review :
Unlike authors who treat thermodynamics as a macroscopic study, Rau uses a ground-up approach, building an understanding of thermodynamic laws from microscopic statistics. He does this much more directly than authors of other texts do. This book offers a modern perspective on statistical physics and thermodynamics. It provides good explanations and carefully selected problems making it an ideal companion for lectures on these topics. With rare clarity and great insight, the author explicates the difficult subject matter of statistical mechanics and thermodynamics in eight compact chapters, from basic concepts to applications to phase transitions. His approach is both logical and systematic -- and is timely with the advent of the quantum information era. This is not just another textbook on statistical thermodynamics because Jochen Rau manages to follow the logical path from quantum mechanics and information theory to statistical mechanics, thermodynamics, and practical applications with great clarity and competence. For students of physics, this concise textbook will be equally stimulating and rewarding. What makes this book special is the cleverly chosen order in which the reader is walked through the fascinating landscape of statistical physics and thermodynamics. The route taken offers a modern overall perspective as well as a thorough understanding of how the different pieces fit together. With a powerful blend of the abstract and the concrete, Rau beautifully reveals how physical consequences emerge from their underlying statistical and quantum mechanical foundations. The writing is crisp and concise, the pedagogy clear and effective. Statistical Physics and Thermodynamics is the fruit of several years of lecturing a very successful course at Ulm University. Jochen Rau's love for teaching is reflected in the careful preparation of this book and becomes apparent when reading it. Indeed, he invested much effort in its preparation and delivered the course with great enthusiasm and engagement, so much so that he was awarded the Goldene Kreide "golden chalk", an award given by students to best lecturer of the semester.