Frisky mule can give you a eureka feeling

Statistical Mechanics. First edition - Statistical Mechanics Made Simple. First edition
November 28, 2003

These are two very attractive and readable books. While they both conform to the now standard high-quality Tex format used in science and mathematics books, the content of each is unique. Both manage to communicate the excitement and intellectual subtlety characteristic of statistical mechanics.

The remarkable thing is that general aspects of macroscopic phenomena can be understood by applying some simple concepts of a statistical nature to the myriad particles that make up macroscopic systems.

Often, we are told that fundamental research consists of taking things apart. We have gone from atoms to protons and electrons, onto quakes and gluons, arriving at strings and the "theory of everything". In the process, we have more or less lost contact with experimental reality.

These two books beautifully demonstrate the other fertile field of fundamental research, that consists of discovering the emergent laws acting at the level of cooperative phenomena involving many particles. The books present plenty of examples of how the struggle to perform the synthesis from the microscopic to the macroscopic involves the development of sophisticated new concepts.

One exciting instance was when Gibbs realised, well before the arrival of quantum mechanics, that he could not describe a non-interacting ideal gas correctly unless he assumed micro-particles to be without individuality. By doing statistical mechanics, Gibbs had stumbled on the quantum-mechanical concept of indistinguishable particles, but long before quantum mechanics.

Franz Schwabl's book is inclined to the more classical aspects of statistical mechanics, spanning the spectrum from traditional thermodynamics to modern topics such as the renormalisation group, percolation and fractal objects. Everything is worked out in minute detail with enjoyable discussions, such as that on the statistical meaning of heat. Each chapter ends with a set of interesting problems. After a brief mathematical introduction, Schwabl covers in detail the background, consisting of equilibrium ensembles and standard thermodynamics. He continues with a thorough discussion of gases and liquids, magnetism and phase transitions.

Then follow equations of motion, such as the Langevin and the Boltzmann equations leading to irreversibility and approach to equilibrium.

Daniel Mattis' book is only half the size of Schwabl's and, accordingly, takes a broader approach. But he manages to present an impressive amount of material. He leans more towards the quantum theory of matter with detailed discussions of bosons, Bose-Einstein condensation and the relation to super-fluidity. Fermions, superconductivity, kinetic theory and conductivity are all covered with enthusiasm. He closes with a chapter on using quantum field theory in statistical mechanics.

It is a joy to read a book by Mattis. He loves physics and science in general, and statistical mechanics in particular. And he loves writing books about the subject, so we get bits of incongruous information here and there. For example, the great Poisson discovered his distribution when, during the Napoleonic wars, he was asked to investigate "the tragic, albeit uncommon, problem of soldiers kicked to death by mules".

These books not only make for a very good read, they also have much to offer advanced undergraduate as well as graduate students. Researchers will likewise find ample inspiration and clear thought. Like good literature, they can be read at different levels by different people.

Henrik Jeldtoft Jensen is professor of mathematical physics, Imperial College London.

Statistical Mechanics. First edition

Author - Franz Schwabl
Publisher - Springer
Pages - 573
Price - £46.00
ISBN - 3 540 43163 2

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