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Mathematical Statistical Mechanics (Princeton Legacy Library), by Colin J. Thompson
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While most introductions to statistical mechanics are either too mathematical or too physical, Colin Thompson's book combines mathematical rigor with familiar physical materials. Following introductory chapters on kinetic theory, thermodynamics, the Gibbs ensembles, and the thermodynamic limit, later chapters discuss the classical theories of phase transitions, the Ising model, algebraic methods and combinatorial methods for solving the two-dimensional model in zero field, and some applications of the Ising model to biology.
Originally published in 1979.
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
- Sales Rank: #5577806 in Books
- Published on: 2015-03-08
- Released on: 2015-03-08
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x .65" w x 6.00" l, .90 pounds
- Binding: Paperback
- 290 pages
Most helpful customer reviews
7 of 7 people found the following review helpful.
Elementary introduction
By Dr. Lee D. Carlson
This book gives an informal overview of the mathematical formalism of statistical mechanics with mathematical rigour not emphasized. There have been many developments in mathematical statistical mechanics since this book was published, particularly in the area of exactly solved models in statistical mechanics and vertex models. This book could be used as an introduction to these developments, in spite of the fact that the mathematics used in them is not covered in this book. Only very rudimentary mathematical tools are used therein. That is not to say that a beginning student interested in the mathematical aspects of statistical mechanics could not gain anything from the reading of the book. There are some very clear presentations of the following topics: 1. A detailed derivation of the Boltzmann equation. 2. A proof of the Poincare theorem, which states that a finite-energy mechanical system in a finite volume is recurrent. 3. A proof of the Liouville theorem, which gives the incompressibility of the flow of points in phase space. 4. A proof, using the Boltzmann "Stosszahlansatz", that the Kac ring model approaches equilibrium. 5. A proof of the existence of the thermodynamic limit for "van Hove potentials", i.e. those that have a hard core and an attractive tail. 6. The explicit calculation of the partition function for the Tonks and Takahashi gases, the Curie-Weiss model, and the one-dimensional Ising model. 7. The Onsager solution of the two-dimensional Ising model. 8. The combinatorial solution of the two-dimensional Ising model. 9. An Ising model for the DNA molecule.
3 of 3 people found the following review helpful.
Mathematical Statistical Mechanics by Colin J Thompson
By Lancia Carlo
This is a very interesting book. The author introduces Classical Statistical Mechanics through several historical examples (Boltzmann distribution, Maxwell distribution, etc.) then he gives an axiomatic interpretation of micro-canonical, canonical and grand-canonical distribution. Last chapters are dedicated instead to applications of Statistical Mechanics in Natural Sciences (expecially in Biology).
The mathematical skills required to the reader are not high although he's supposed to be quite "independent" to develop all the calculations by his own.
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