This is not the first book entitled Modern Thermodynamics, but it is certainly a book from a very uncommon viewpoint for thermodynamics: the information theory proposed by Claude E. Shannon in 1948 (Bell Syst. Tech. J. 27 (3), 379). Ben-Naim and Casadei have written this book presenting their systematic research on the link between information theory and thermodynamic entropy.
The book is divided into two sections: Fundamentals and Applications. Eight chapters cover the fundamentals, and four chapters cover specific applications. The first two chapters provide a brief historical development of thermodynamics and information theory. Perhaps the most interesting subsection is The Basic Idea of Information Theory, which is presented using a question game to find an unknown subject, person, or thing. The third chapter introduces the elements of probability theory, which are required to fully understand the concepts of Shannon’s Measure of Information (SMI), called “entropy.” The authors argue that SMI is definitely different from thermodynamic entropy because it is more general. They use the axiomatic approach to probability and introduce the three major probability distributions (uniform, exponential, and normal) that are required for deducing the ideal gas entropy. Chapters 4 and 5 pre-sent the principal theorems behind SMI, which are related to the defined probability distribution functions. They also provide an important discussion on the interpretation of SMI and its maximum value, which is associated with the most probable distribution, the equilibrium distribution density.
Chapters 6 and 7 represent the heart of the book: the deduction of the entropy of an ideal gas from SMI and the interpretation of the entropy change for some spontaneous processes in terms of SMI. These chapters argue that SMI provides the same function for the entropy of an ideal gas apart from a multiplicative constant, hence the entropy of an ideal gas is a measure of the information distributed among the gas particles: their number, energy, and volume. The last chapter of the first part deals with the basic formalism of thermodynamics and generalizes the previous theory with some constraints.
The second part of the book, chapters 9 to 12, presents thermodynamic applications on phase rule, phase diagram, mixtures and solutions, chemical equilibrium, pure water, and water solutions. The chapter on phase rule and phase diagrams covers the derivation of the Gibb’s phase rule and its application for non-reacting and reacting systems, the coexistence of two phases in one-component systems, and a brief description of the two-component system. The chapter on mixtures and solutions provides an unusual approach to the thermodynamics of solutions using the pair correlation function (i.e., radial distribution function) and the Kirkwood–Buff theory to explain some properties and the interaction between different solute molecules with their environment. The chapter on chemical equilibrium derives the general equilibrium condition for a reaction and its dependence on pressure and temperature. The final chapter is devoted to water and aqueous solutions. It presents the different water phases and water properties as an equilibrium mixture of two species with low and high local density.
Edwin T. Jaynes provided the first connection of SMI to statistical thermodynamics in 1957 (Phys. Rev. 106 (4), 630). It was a mathematical approach without simple examples. Ben-Naim and Casadei have provided a more didactic approach. This book may not be considered a textbook for a normal graduate course on thermodynamics, though there are exercises throughout the book with solutions in the appendix. The figures are simple, but they provide important support for the text. The references are adequate. This book is a must for physicists, chemists, engineers, and people with some knowledge of mathematics who want to deepen their understanding of thermodynamic entropy and applications.
Reviewer: Roberto Ribeiro de Avillez of the Pontifícia Universidade Católica do Rio de Janeiro, Brazil.
