Thermodynamics: For Physicists, Chemists and Materials Scientists, Reinhard Hentschke, Springer, 2014. $59.95 paper (304 pp.). ISBN 978-3-642-36710-6 Buy at Amazon

Thermodynamics can be a tough sell in the classroom. “Many of us associate thermodynamics with blotchy photographs of men in old-fashioned garments posing in front of ponderous steam engines,” writes Reinhard Hentschke in the preface to his new textbook, *Thermodynamics: For Physicists, Chemists and Materials Scientists*. Hentschke is a professor of theoretical chemical physics and a practitioner of thermodynamics. His research expertise in soft-matter physics informs many of the examples that bring the book to life. With this volume of concise theoretical developments and numerous, detailed applications, the author shows that mastering thermodynamics is indispensable for understanding properties and processes at finite temperature. It should provide ample motivation for students hoping to contribute to the development of new materials and technologies.

The book’s seven chapters can be roughly divided into four sections: introduction to thermodynamics, phase equilibria and phase transitions, statistical mechanics and computer simulations, and nonequilibrium thermodynamics. The introduction to thermodynamics follows the traditional route, from the concepts of work and the laws of thermodynamics to formal definitions of temperature and entropy and the introduction of thermodynamic functions and free energies. The author derives work expressions for a wide range of systems, including elastic solids and dielectric media, thereby preparing the reader for the diverse applications that follow in later chapters.

Phase equilibria and phase transitions form the book’s central portion, which contains well-constructed examples that guide the reader as the treatment becomes more sophisticated. Those topics build a solid foundation for soft-matter physics, and the interested reader will find good references to the more specialized literature. The van der Waals equation of state serves as the introduction to phase transitions and to the limitations of theories that neglect fluctuations in the critical region. Returning to classical (mean-field-type) equations of state, Hentschke discusses phase diagrams for superconductors and simple and complex fluids. A lecturer teaching those examples may want to add a section that emphasizes the common aspects of systems undergoing phase transitions, identifies order parameters and ordering fields, and perhaps shows how the examples relate to the Landau theory of phase transitions.

The chapters on statistical mechanics and computer simulations provide the connection between the macroscopic scale of thermodynamics and the microscopic scale of molecular interactions. In that section, the applications illustrate and extend earlier examples treated with thermodynamic tools and introduce computational techniques to investigate phase coexistence. The Monte Carlo algorithms presented in the book are quite sophisticated and may persuade students who enjoy computational work to study the underlying thermodynamic and statistical mechanics concepts.

The book’s final chapter is a brief introduction to nonequilibrium thermodynamics. To illustrate linear transport theory and Onsager’s reciprocity relations, the author includes the Seebeck and Peltier effects from solid-state theory. Chemical reactions are the basis of examples for the challenging subjects of minimum entropy production in the steady state and dynamics of complex systems.

The book’s approach to thermodynamics is concise and application oriented. Readers looking for broader discussions of the general principles of thermodynamics may be better served by two of the classic texts: A. B. Pippard’s *The Elements of Classical Thermodynamics* (Cambridge University Press, 1957) and Herbert Callen’s *Thermodynamics and an Introduction to Thermostatistics* (Wiley, 1985). Although Hentschke’s presentation is complete, a stronger focus on the general formalism—emphasizing such concepts as thermodynamic densities and fields and distinguishing between thermodynamic potentials and equations of state—would have provided context for the specific cases addressed in the book and would have made it easier for readers to go beyond the large range of systems it discusses.

Consistent with the style of exposition, the level of mathematics in the book is higher than in such popular undergraduate texts as Ralph Baierlein’s *Thermal Physics* (Cambridge University Press, 1999) and Daniel Schroeder’s *An Introduction to Thermal Physics* (Addison-Wesley, 2000). To take full advantage of the material, the reader should be familiar with classical mechanics and electrodynamics at the undergraduate level and, ideally, have studied some chemistry. With its carefully worked examples on a wide range of topics, Hentschke’s *Thermodynamics* is a valuable resource for students and faculty of statistical mechanics courses at the advanced-undergraduate or graduate level.

**Jutta Luettmer-Strathmann** is an associate professor of physics and chemistry at the University of Akron in Akron, Ohio. She investigates soft condensed matter using theoretical and computational tools.