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an introduction to statistical mechanics and thermodynamics

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In preparing to write the preface to the second edition of this book, I realized anew my debt to the work of Herbert B. Callen. He was not only my thesis advisor and my friend, but it was through his teaching and his book on thermodynamics that I first understood the subject in any depth. I take this opportunity once again to acknowledge how much his pedagogy and advice have meant to my work. The postulational approach to thermodynamics, which is primarily based on his work and that of his thesis advisor, László Tisza, provides a clear basis for the theory. 

It is not difficult to understand but can seem rather abstract when first encountered as a student – as, indeed, it did to me many years ago. Many professors have told me that they thought that Callen’s book was too daunting to give to their students, but that it was the book that they consulted for thermodynamics. 

Part I of my book originated as an introduction to Callen’sThermodynamicsin my teaching. One difficulty that I had found as a student was that Callen’s book started off presenting entropy and the postulates of thermodynamics in the first chapter, and temperature as a partial derivative of the entropy in the second chapter.

 I had only a vague idea at the time of what the entropy was, and its partial derivative with respect to energy was a complete mystery. I have tried to avoid this difficulty in my own teaching of thermodynamics by presenting the students with an explicit calculation of the entropy of a classical ideal gas.

 All assumptions are stated, and all mathematics is explained. I felt – and my students generally agreed – that they were then ready to understand Callen’s postulates. Part II developed from my notes for teaching from Callen’s textbook. I found that while the ideas in Callen’s postulates provided a great foundation for thermodynamics, their specific form was less than ideal.

 For the first edition of this book, I separated them into six new postulates, each of which expressed a separate idea. I also generalized the postulates to include non-homogeneous systems.

 I gave an explicit guide to the use of Jacobians in deriving thermodynamic identities, which I have not found anywhere else, but which my students have found to be easy to apply. Callen mentioned Jacobians in his first edition, but not in his second. Similarly, I simplified the derivation of Maxwell relations, with the result that my students have regarded them (correctly) as being easy to derive.

 I also gave an explicit derivation of the stability criteria for second partial derivatives with respect to intensive variables because many students had difficulty with them. Parts III (classical statistical mechanics) and IV (quantum statistical mechanics) used computer calculations extensively. They allowed many calculations to be carried out explicitly. I firmly believe that the future of physics will rely heavily on the computer, and I think that computation is currently being neglected in university curricula.

The second edition has come into being because I have discovered how to clarify the presentation of many of the central concepts, especially in the derivation of the entropy in Part 1. Along the way, I have corrected a significant number of typographical errors. In Part I, Chapters 4 and 6, I have more clearly distinguished generic variables from variables describing particular systems used in derivations. 

My previous labeling convention did not cause any problems in the classes I taught, but it has caused confusion with some readers. I have also generalized the derivation of the entropy from treating only two systems at a time to deriving the entropy simultaneously for all systems that might interact. In the second edition, I have again changed the list of postulates to include the possibility of negative temperatures. Callen had mentioned negative temperatures in his book, but had excluded them in the interest of simplicity. In Chapter 11, I have expanded the review of the Carnot cycle with two new illustrations.

 This chapter now also contains a discussion of negative temperatures, and how they affect the analysis of heat engines. Massieu functions were mentioned by Callen, but not developed. I did the same in the first edition. 

I have expanded the treatment of Massieu functions in Chapter 12, after realizing that they are much more useful than I had previously thought. They are essential when considering negative temperatures because the corresponding entropy is not monotonic. The discussion of the Nernst Postulate (Third Law of Thermodynamics) in Chapter 18 includes a discussion of why zero temperature would not be possible to attain if classical mechanics were valid instead of quantum mechanics. 

In fact, it would be more difficult to attain very low temperatures if the Nernst Postulate were not valid. A new chapter (Chapter 21) has been added to discuss the consequences of including the widths of the energy and particle-number distributions in the calculation of the entropy.

 It is both a more realistic assumption and gives better expressions for the entropy. These results are based on new work since the publication of the first edition of this book. In Chapters 28 on Bose-Einstein statistics and 29 on Fermi-Dirac statistics, I’ve introduced numerical calculations based on work with a former student, Tyson Price. 

The numerical results show many of the thermal properties of Bose and Fermi gases more clearly and simply than would be possible with analytic calculations alone. The Index has been thoroughly updated and expanded. My recommendations for a programming language to use for the computational problems have changed. I still advocate the use of Python, although not VPython. 

I have found that plots using MatPlotLib are much better, as well as being easier for students (and professors) to program. On the other hand, I have found that students prefer the freedom to use a wide variety of programming languages, and I have never insisted that they use Python. 

I would like to thank my colleagues, Markus Deserno and Michael Widom, for their helpful comments based on their own experiences from using my book to teach both undergraduate and graduate courses in thermal physics. 

I would also like to thank my former students, William Griffin, Lachlan Lancaster, and Michael Matty, for their contributions to some of the results presented here. I would especially like to thank Michael Matty for his extensive constructive criticism of the text and his contributions to my class.

 Finally, I would like to thank Karpur Shukla for many useful conversations. As in the first preface, I would like to thank my wife, Roberta L. Klatzky, for her unwavering support.