Entropy is a difficult concept to understand. Even if a student has the necessary mathematical background to follow the derivations associated with applying entropy in different contexts, it is not easy to develop an intuition about what entropy is. In A Student's Guide to Entropy, Don Lemons conveys both mathematical and physical intuition of entropy.
The concept of entropy is present in the sciences, engineering, and other areas (e.g., economics). Etymologically, entropy is derived from the Greek words en (meaning in) and tropē (meaning turn), and thus it was developed in an effort to describe how systems “turn” or evolve in time. Since many disciplines are interested in describing system dynamics, the ubiquity of entropy makes it a concept that is essential for students of these disciplines to comprehend and appreciate. To these students, this book will be very helpful.
The book provides an illuminating overview of the concept of entropy. Each chapter deals with a different aspect or application of entropy: thermodynamic and statistical entropy (chapters 1 and 2), entropy of classical and quantized systems (chapters 3 and 4), entropy of a non-isolated system (chapter 5), entropy of fermion and boson systems (chapters 6 and 7), and entropy of information (chapter 8). The book also contains six appendices. However, the words overview and guide might be misleading since they might imply a lack of depth for the benefit of breadth. On the contrary, the author is very thorough, clear, and succinct in his explanations, making sure that no subtlety is left unnoticed or unaccounted for. The reader feels that he/she is being taught and guided by an experienced teacher of thermodynamics and entropy, its applications and subtleties (Lemons has written another textbook in the field called Mere Thermodynamics). This book will be essential not only to students but also to faculty who are charged with the difficult task of teaching a subject that involves entropy.
There are two aspects of this book that I particularly liked. The first is that the author does not shy away from the mathematics; this book can by no means be considered light reading. Entropy is a highly mathematically driven subject. As such, the mathematics is essential for the development of understanding and intuition about the concept. Consequently, upper-level undergraduate students, who have a very good foundation in algebra, calculus, differential equations, and probability and statistics, will make the most out of the book. The author works through the mathematical derivations, letting the reader connect some of the dots, presents examples in the text, and also provides problems at the end of each chapter. The answers to these problems are given in an appendix (Appendix V). However, the book does not contain step-by-step solutions to these problems. This is the only element in the book that readers, especially those who intend to use this book for the purpose of self-study, might find disappointing.
The second contributing element to the book's success, one which the author often uses in his books, is his choice to provide a historical outline of entropy. This outline includes a timeline in Appendix IV. Lemons uses this tool in order to provide the reader not only with a lesson in history, but also with a lesson in physics. The history of thought behind entropy allows the author to point out the shortcomings of ideas that had already been developed and the reasons behind the need for their expansion or the formation of new ones in order to answer additional questions. Thus, through this historical overview, the author helps the reader look at entropy critically and from a different perspective, as all the famous physicists (e.g., Carnot, Boltzmann, etc.) had done in the past. This helps the reader develop physical and mathematical insight and intuition. Furthermore, regardless of whether one thinks of entropy as disorder, uncertainty, or possibility, with the last being the author's “favorite short description of entropy,” the author manages to explain the reasons behind these synonyms for entropy using physical, mathematical, and historical justifications. In addition to the timeline, other delightful elements of the book are the inclusion of a glossary of terms (Appendix III) and a comprehensive reading list (Appendix VI).
In A Student's Guide to Entropy, the author has succeeded in writing a book that “helps readers understand the elusive concept of entropy.” The book goes beyond that by helping the reader acquire an appreciation for entropy. It is a thorough, self-contained guide to entropy for students and teachers alike.
Effrosyni Seitaridou is Associate Professor of Physics at Oxford College of Emory University. Her research focuses on diffusion in biological systems.
