Many--- might I say most--- physics textbooks have major flaws. Some have no worked examples in the text. Some have partial or no derivations (cf. the evil "derivation left to the reader.") Others have no practice problems. Of those that do have problems, many don't provide solutions. Finally, many are extremely obtuse in their explanations; they simply can't explain things well.

This textbook, "A Student's Guide to Entropy" by Don S. Lemons, avoids (almost) all of these pitfalls. Other than one minor reservation that I have (which I'll mention later,) I felt that this was an almost perfect example of what a good textbook should be! (You do need integral and derivative calculus and an understanding of infinite series; if you don't have an understanding of this math, this book is not for you.)

The author (an emeritus professor of physics) has spent many years doing research on the very topics in this book. While that is certainly a good thing--- he's an expert, and it's nice knowing that you're learning from an expert--- it is not a SUFFICIENT thing for writing a good textbook. What is needed, really, is an understanding and memory of what it was like BEFORE you understood those things you're an expert in--- and the ability to explain these topics clearly to those who don't yet understand them. Many experts have no ability at all to explain or convey their ideas in this fashion. Don Lemons does.

Here are the details:

The topic of the book is entropy (duh!) Entropy is one of the slipperiest concepts in physics. It has several definitions which seem, at first, to not be related to one another. For example, entropy is necessary to understand heat engines and the thermodynamic states of classical systems (like your car engine,) but is also needed to understand weird quantum states of matter like Bose-Einstein condensates. Just when you think you understand how the pressure inside a piston is related to Bose-Einstein condensation, then you learn that actually all of these ideas are the same as those in information theory and computer systems. Weird, right? Because this idea is so pervasive in so many different areas of science and physics, and yet because it looks different on the surface when you use it in these different fields, it can quickly get out of hand when you attempt to truly understand what the heck it means. I've tried to read several other textbooks on this quite difficult topic, only to become quickly lost. Not so with this book!

It is obvious that this author has thought very long and very hard about what would be the best and clearest and simplest way to present this topic. I can say with some great relief that he has succeeded brilliantly!

The book starts with a discussion of classical thermodynamic systems. He doesn't expect too much prior knowledge here, and very clearly defines what he means at each stage. Reversible and irreversible systems, heat engines, the laws of thermodynamics... and then discusses how entropy fits in. From there he moves on in subsequent chapters to Statistical Entropy, Entropy of Classical Systems, Entropy of Quantized Systems, Entropy of Non-Isolated Systems (and the dreaded partition function,) Entropy of Quantum Systems (Bose and Fermi Systems,) and concludes with a chapter on the Entropy of Information. This is a short, excellent, clear overview of the main areas in physics where entropy plays a key role.

What I appreciate most about his writing style is that he clearly DEFINES new ideas in words before presenting formulas, but doesn't get too off track on side topics. Everything that he presents is really the essential nugget of the topic without extraneous jibber-jabber. Additionally-- and I can't emphasize this enough-- he really has a gift for explanation. Some topics that, in the past, I didn't quite grasp fully I feel that I have a much better handle on after reading this book.

Besides his skills at exposition, the way he chose to structure the book is generally excellent. He provides worked examples in the text, and then provides practice exercises at the end of each chapter. He provides the numerical solutions for these examples at the end of the book. He provides an extensive glossary, as well as a reading list. These are all great things.

Here is the one caveat that I mentioned I had earlier, though: While providing numerical solutions is helpful (and certainly better than nothing,) I would have much preferred these to be WORKED, STEP-BY-STEP solutions. While I understand that he might not have had room to do this in the textbook itself, I urge Professor Lemon to consider providing WORKED solutions to all of these problems on his website or in a downloadable PDF. That would have helped me tremendously! (In order to truly understand how to do physics, you simply HAVE to be able to do problems. If you don't have access to a professor or graduate student, there is really no way to find the solution to a problem if you just can't crack it on your own. If you don't have a solution to work through, you're stuck--- and it stops you from moving forward in your learning. A solutions manual would help avoid that.)

One other (small) complaint I have is that there are several homework problems of the type "Derive Equation 16." I hate these type of problems; almost every author of a physics text does this, and I wish they'd stop it. Just give me the derivation already! That's what a text should provide. A derivation is an explanation of how the physics came to be understood--- and that is what a textbook should be giving you. That is what you need to truly understand the topic. You, as a student, shouldn't have to work this out yourself! Using the conclusions of those derivations is what the homework should be about. <endrant>

Besides those two minor quibbles, I think this is quite an excellent textbook for those interested in learning the physics of entropy. I learned quite a lot, and felt that I was being guided with great care by a concerned and empathetic expert.

I would recommend it!