Statistical Mechanics: Entropy, Order Parameters, and Complexity

The purview of science grows rapidly with time. It is the responsibility of each generation to join new insights to old wisdom, and to distill the key ideas for the next generation. This is the author’s distillation of the last fifty years of statistical mechanics’a period of grand synthesis and great expansion.

This text is careful to address the interests and background not only of physicists, but of sophisticated students and researchers in mathematics, biology, engineering, computer science, and the social sciences. It therefore does not presume an extensive background in physics, and (except for Chapter 7) explicitly does not assume that the reader knows or cares about quantum mechanics. The text treats the intersection of the interests of all of these groups, while the exercises encompass the union of interests. Statistical mechanics will be taught in all of these fields of science in the next generation, whether wholesale or piecemeal by field. By making statistical mechanics useful and comprehensible to a variety of fields, we enrich the subject for those with backgrounds in physics. Indeed, many physicists in their later careers are now taking excursions into these other disciplines.

To make room for these new concepts and applications, much has been pruned. Thermodynamics no longer holds its traditional key role in physics. Like fluid mechanics in the last generation, it remains incredibly useful in certain areas, but researchers in those areas quickly learn it for themselves. Thermodynamics also has not had significant impact in subjects far removed from physics and chemistry: nobody finds Maxwell relations for the stock market, or Clausius’Clapeyron equations applicable to compression algorithms. These and other important topics in thermodynamics have been incorporated into a few key exercises. Similarly, most statistical mechanics texts rest upon examples drawn from condensed matter physics and physical chemistry-examples which are then treated more completely in other courses. Even I, a condensedmatter physicist, find the collapse of white dwarfs more fun than the low-temperature specific heat of metals, and the entropy of card shuffling still more entertaining.

This text is aimed for use by upper-level undergraduates and graduate students. A scientifically sophisticated reader with a familiarity with partial derivatives and introductory classical mechanics should find this text accessible, except for Chapter 4 (which demands Hamiltonian mechanics), Chapter 7 (quantum mechanics), Section 8.2 (linear algebra), and Chapter 10 (Fourier methods, introduced in the Appendix). An undergraduate one-semester course might cover Chapters 1-3, 5-7, and 9.