Upon receiving a copy of Roberto Piazza’s new book, I was immediately intrigued by the title, Statistical Physics: A Prelude and Fugue for Engineers. I have to admit that the whimsy of the title evinced a slight suspicion that Piazza’s treatment of a deep scientific topic might be given over to periodic flights of fancy. But, as the saying goes, you shouldn’t judge a book by its cover, and, happily, I found my worries were not realized.
Johann Sebastian Bach was a master of counterpoint, a compositional technique that weaves together interdependent voices. The intricate music that emerges is characterized by an unmistakable economy of form. Piazza’s treatment of statistical physics is also frugal in the best sense of that word. The book is billed as a text that will meet the needs of graduate students in chemical, mechanical, and materials science engineering, and it succeeds in that objective.
Statistical Physics begins with a discussion of classical thermodynamics followed by an introduction to the fundamental ideas behind statistical thermodynamics. It then builds to an exploration of quantum statistics. The transition from one section to another is natural and unlabored. Piazza’s analyses are comprehensive and entertaining, yet they remain uncluttered, and they prompt serious reflection. Interspersed throughout the book are frequent anecdotal asides featuring Ludwig Boltzmann, James Clerk Maxwell, Sadi Carnot, Lord Kelvin, and other distinguished historical figures in the field. To repeat an oft-stated aphorism, they are the giants on whose shoulders all statistical physicists stand.
The classical thermodynamics of the first two chapters covers standard fare, including the first, second, and third laws; reversibility; the Clausius theorem; free energy; and the Gibbs paradox. The discussion of entropy and its significance is particularly well done. In many introductory texts, that classical material is not given the subtle treatment it deserves and, in my experience, leaves students wondering just what all the fuss is about. Piazza manages to avoid that pitfall. I would, however, have liked to see Legendre transforms discussed, since without them students may wonder just how enthalpy and the Helmholtz and Gibbs free-energy expressions seem to appear out of thin air. As is the case throughout the text, Piazza’s little discursions from the main topic are often illuminating. A good example is the discussion on page 28 of the relationship between speed and irreversibility in an idealized heat engine.
The middle part of the book, chapters 3–5, applies the basic tenets of statistical physics to build important models that include the van der Waals equation of state, the Einstein model for the specific heat of a solid, and the Debye–Hückel equation. In many other texts, the material is discussed with an intimidating formalism that hides the underlying concepts and forces students to struggle with the mathematics instead of spending time reflecting on the often enigmatic nature of the subject. Piazza, however, encourages students to both master the mathematics and grapple with the subject’s fundamental principles.
In chapter 3, for example, the material moves seamlessly from the canonical distribution function to the application of that function to simple classical and quantum systems, including paramagnetic systems. The well-done discussion of the inconsistency between the predictions of the Einstein model and experimental data for specific heat close to absolute zero temperature is interspersed with intermezzos of delightful anecdotes about the work of earlier scientific pioneers.
Chapters 4 and 5 cover the application of statistical physics to fluids and ferromagnetic systems. The material is standard, but the author’s treatment is refreshing. It includes a simple exposition that uses the classical partition function to derive the van der Waals equation of state along with more sophisticated discussions of, among other things, the Poisson–Boltzmann equation, critical phenomena in the Landau–Ginzburg model, and elementary considerations of the renormalization-group approach. Chapter 6 belatedly introduces the grand canonical ensemble and its application to adsorption and colloids. It is the skimpiest part of the book, an interlude, before chapter 7, which focuses on quantum phenomena like Bose–Einstein condensation and superfluidity. Once again, the material, which will be especially useful to students of materials science engineering, is covered in many books, but the author’s presentation is excellent.
Piazza’s book is a welcome addition to the statistical-physics canon. There are no sample problems to hone one’s understanding of the material, however, so for a fuller appreciation of the book, I recommend that students first practice their scales by completing introductory courses in thermodynamics and quantum mechanics. Once that is achieved, Piazza’s choice of material and his lucid presentation of abstract, sometimes difficult concepts will make for instructive and enjoyable reading.
Eldred Chimowitz is a professor of chemical engineering at the University of Rochester. He is the author of Introduction to Critical Phenomena in Fluids (Oxford University Press, 2005) and the novel Between the Menorah and the Fever Tree (CreateSpace, 2010).