An Introduction to Statistical Mechanics and Thermodynamics
DOI: 10.1063/PT.3.2087
The development of statistical mechanics—understanding a macroscopic system through a statistical analysis of its microscopic properties—is one of science’s great intellectual achievements. That approach has had a wide-ranging impact on our understanding of many-body systems in the physical and biological sciences and in such fields as economics and information theory. The need is growing for an introduction to statistical and thermal physics, which also includes modern computational methods.
In his innovative new text, An Introduction to Statistical Mechanics and Thermodynamics, Carnegie Mellon University physics professor Robert Swendsen presents the foundations of statistical mechanics with, as he puts it, a detour through thermodynamics. That’s a desirable strategy because the statistical approach is more fundamental than the classical thermodynamics approach and has many applications to current research problems. The book’s focus is on the development of the main theoretical concepts important to understanding equilibrium systems (although much of the current research in statistical physics is on nonequilibrium systems). The organization of the material is different from most texts on thermal physics—another term for the combined study of thermodynamics and statistical mechanics.
The book, which grew out of Swendsen’s two-semester course at Carnegie Mellon, is divided into four parts. The first introduces Boltzmann’s entropy definition as the logarithm of the probability of a macroscopic state, develops the related mathematical background, and calculates the entropy of a classical ideal gas. With his interpretation of Boltzmann’s definition, Swendsen avoids paradoxes associated with distinguishable and indistinguishable particles. It also allows him to avoid the apparent violation of the second law of thermodynamics in closed systems, in which the entropy is defined as the logarithm of the volume of accessible phase space.
The second part begins with the formal postulates and laws of thermodynamics. In delaying the introduction of the general thermodynamic postulates, Swendsen is able to build on his earlier discussion of entropy, the example of the ideal gas, and the thermodynamic limit. In part three, the discussion focuses on the various ensembles of statistical mechanics and on computer simulations of classical systems, and in part four, it centers on quantum statistical mechanics and properties of materials. Applications to semiconductors and the Ising model are discussed toward the end of the book.
Theoretically inclined students will find An Introduction to Statistical Mechanics and Thermodynamics highly rewarding because it develops the more general concepts first, makes few assumptions, and develops its consequences as theoretical physicists like to do. Students who have had no previous exposure to thermal physics and those who are motivated more by observations and experiments are likely to find the material too abstract.
An Introduction to Statistical Mechanics and Thermodynamics has few illustrative examples to illuminate the abstract concepts discussed or to inspire students to tackle the material. It contains few figures; for instance, it does not include the usual flow charts for various engine cycles. For those reasons, additional exercises would be useful, especially for undergraduate students who have seldom encountered probability in a previous science course and who are grappling with multidimensional calculus.
Swendsen has made many important contributions to developing Monte Carlo algorithms, and it is not surprising that he emphasizes computational applications. A brief appendix on computer calculations and the programming language VPython can be found at the end of the book, and many of the problems at the end of chapters are computational. The author assumes students will have a reasonable proficiency in computational physics; those who are not already proficient will be challenged to learn the necessary techniques while simultaneously tackling the physics and mathematical concepts newly encountered in statistical physics. Surprisingly, random walks are not mentioned, even though they are important for gaining an intuitive understanding of random processes. Kinetic theory is also not discussed.
Although I do not envision that An Introduction to Statistical Mechanics and Thermodynamics will be used as a primary text for the more typical one-semester undergraduate course on thermodynamics and statistical physics, the book would be a helpful companion textbook. The mathematical notation is carefully introduced and useful; the selected mathematical techniques are clearly explained in a conversational style that both graduate and advanced undergraduate students will find easy to follow. The author’s subject organization and conceptual viewpoint address some of the shortcomings of conventional developments of thermal physics and will be helpful to students and researchers seeking a deep appreciation of statistical physics.
More about the Authors
Arshad Kudrolli is a professor of physics at Clark University in Worcester, Massachusetts. He does experiments on a broad range of nonequilibrium phenomena, including statistical-physics approaches to nonequilibrium phenomena in granular materials.
Arshad Kudrolli. Clark University, Worcester, Massachusetts.
