Energy and Entropy : A Dynamic Duo book cover
1st Edition

Energy and Entropy
A Dynamic Duo

ISBN 9780367349066
Published August 27, 2020 by CRC Press
328 Pages 180 B/W Illustrations


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Book Description

Energy is typically regarded as understandable, despite its multiple forms of storage and transfer. Entropy, however, is an enigma, in part because of the common view that it represents disorder. That view is flawed and hides entropy’s connection with energy. In fact, macroscopic matter stores internal energy, and that matter’s entropy is determined by how the energy is stored. Energy and entropy are intimately linked.

Energy and Entropy: A Dynamic Duo illuminates connections between energy and entropy for students, teachers, and researchers. Conceptual understanding is emphasised where possible through examples, analogies, figures, and key points.


  • Qualitative demonstration that entropy is linked to spatial and temporal energy spreading, with equilibrium corresponding to the most equitable distribution of energy, which corresponds to maximum entropy
  • Analysis of energy and entropy of matter and photons, with examples ranging from rubber bands, cryogenic cooling, and incandescent lamps to Hawking radiation of black holes
  • Unique coverage of numerical entropy, the 3rd law of thermodynamics, entropic force, dimensionless entropy, free energy, and fluctuations, from Maxwell's demon to Brownian ratchets, plus attempts to violate the second law of thermodynamics

Table of Contents

Chapter 1. Energy is Universal

Chapter 2. Energy is Not Enough

Chapter 3. Entropy: Energy’s Needed Partner

Chapter 4. Gases, Solids, Polymers

Chapter 5. Radiation and Photons

Chapter 6. Numerical Entropy

Chapter 7. Language and Philosophy of Thermodynamics

Chapter 8. Working, Heating, Cooling

Chapter 9. Sanctity of the 2nd law of Thermodynamics

Chapter 10. Reflections and Extensions

Chapter 11. Appendices: Mathematical Identities

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Harvey S. Leff is Professor Emeritus of Physics at California State Polytechnic University in Pomona, California and Visiting Scholar at Reed College in Portland, Oregon. He has published widely in thermal physics, writing primarily for physics and chemistry teachers and students. With Andrew Rex, Leff co-edited Maxwell's Demon 2: Entropy, Classical and Quantum Information, Computing. He served as President of the American Association of Physics Teachers, and is a Fellow of the American Physical Society and the American Association of Physics Teachers, and a Consulting Editor for the American Journal of Physics. When not doing physics, Leff plays drums in two bands, The Leff Trio and Jazz Up, and he is the former drummer in The Out-Laws of Physics.


"In this book Leff (emer., California State Polytechnic Univ.) intertwines all aspects of energy and entropy through a plethora of subjects, from classical topics such as the Clausius inequality to the relatively new "nonequilibrium equality for free energy differences" as discussed by C. Jarzynski…The author is to be commended for engaging readers in considering the concept of energy and entropy using accessible mathematics. The strength of this book lies in the author's endeavor to create "Key Point" snippets throughout the book. These points are the cream of the crop, accentuating and demystifying important concepts, and empowering the reader to leave each chapter with essential takeaways. Though the book lacks problems and exercises at the end of each chapter, this does not diminish the value of a text that is sure to appear on the bookshelf of confirmed thermodynamicists, and will furnish a possible technical elective for upper-division students in engineering and physics. The volume can also serve as an excellent reference resource for graduate students in engineering and physics with research interests in materials science, biophysical systems, and magnetic nanoparticles in biotechnology, to name a few areas of applicability.
Summing Up: Highly recommended. Upper-division undergraduates. Graduate students, faculty, and professionals."
—R. N. Laoulache, University of Massachusetts Dartmouth in CHOICE November 2021 (Vol. 59 No. 3)

"Not often does one have the chance to read a book that is the result of a lifetime of productive thought about an important subject, but such is the case with Harvey Leff’s Energy and Entropy.  One is astounded by the depth and breadth of this book.  And, what is more, Professor Leff has a deft way of appealing to various kinds of readers:  professionals who want to see the mathematics and those who desire a more conceptual understanding.  If you have room on your bookshelf for only one volume on thermodynamics, (and I don’t say this lightly) your choice should be Energy and Entropy."

— Don S. Lemons, Professor of Physic Emeritus, Bethel College, North Newton, Kansas

"Harvey Leff has used his lifelong interest and expertise in thermodynamics and statistical mechanics to write a delightful monograph on the relation between energy and entropy. The author explains the relation with thoughtful explanations including detailed examples, many of which are glossed over in most thermodynamics texts. Although most of the text is intended to expand on traditional material, more advanced topics such as the Jarznski equality are also discussed. The text should be of particular interest to students who are puzzled by the many subtleties of thermodynamics and by instructors who wish to offer a deeper understanding of the subject."

Harvey Goud, Clark University

"In this volume Harvey Leff has made a unique contribution by illustrating many connections between entropy and energy in a wide range of contexts, both theoretical and practical. The book begins with what is essentially a review of the laws of thermodynamics, with energy featured in connection with the first law and entropy in connection with the second. Although Leff includes the historical underpinnings of thermodynamics going back to the 19th century, he also addresses more contemporary topics such as black hole entropy, Landauer’s principle, the entropy of information and computation, and recent efforts to find violations of the second law. The book contains numerous simple but effective illustrations and graphs. A pedagogical feature that many readers will find effective is the use of “key points” that give a brief synopsis of the preceding section of text. I found that the key points often provide a bridge from one section to the next. This book is highly recommended as a learning tool for professionals and graduate students who seek a more comprehensive and wide-ranging treatment of entropy in its many forms and applications."

 — Andrew Rex, University of Puget Sound

"Energy and Entropy: A Dynamic Duo offers many insights to many different audiences. But Leff rightly identifies "teachers of physics, chemistry, and engineering" first on his list of prospective readers.  Perhaps no other group of scientists has a greater need for a conscience than those of us who teach thermodynamics… Unlike many other books on the subject, Energy and Entropy does not give its reader the impression that thermodynamics is a fully resolved product of the 19th century. Leff demonstrates that significant discoveries have been made since the contributions of Boltzmann and Gibbs. He provides an accessible introduction to the Jarzynski equality. He also traces the many discoveries that were motivated by Maxwell's demon, illustrating how statistical mechanics led to later developments in information theory… Leff is careful throughout his book to emphasize that energy and entropy are equal partners. He also refrains from treating these quantities as abstract concepts. The presentation rarely strays from a plausible experiment. Even the discussion of information theory is rooted in measurable physical quantities.

My overall impression of this book can be characterized by the title of an article that Leff contributed to The Physics Teacher. The title of the article is Thermodynamics Is Easy-I've Learned It Many Times. When reading a good book on the subject, I agree. Thermodynamics can seem easy, particularly when the book is written by a scientist whose previous work has helped to clarify fundamental issues. But as I continue to grapple with the subject, I know that I will continue to find more subtle points in need of explanation. And when those future moments inevitably arrive, Energy and Entropy will be among the books to which I'll turn in order to find my conscience."

 Eric Johnson, Chair of the Department of Chemistry at Mount St. Joseph University, in American Journal of Physics Vol 89, No 7 (2021).