Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics (Cambridge
By addebook • Jul 3rd, 2008 • Category: Mathematics •
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Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics (Cambridge Mathematical Library)
Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics (Cambridge Mathematical Library)
By David Ruelle
Publisher: Cambridge University Press
Number Of Pages: 174
Publication Date: 2004-11-29
ISBN-10 / ASIN: 0521546494
ISBN-13 / EAN: 9780521546492
Binding: Paperback
Reissued in the Cambridge Mathematical Library, this classic book outlines the theory of thermodynamic formalism which was developed to describe the properties of certain physical systems consisting of a large number of subunits. Background material on physics has been collected in appendices to help the reader. Supplementary work is provided in the form of exercises and problems that were “open” at the original time of writing.
Summary: The Mathematics of Thermodynamics
Rating: 4
Rating a book like this is very difficult, because it’s not like anything else. Thermodynamic Formalism is a book on the mathematical analysis of statistical thermodynamics, and its very dense. By “mathematical analysis” I mean the logical derivation of relationships of symbols from abstract definitions. Therefore, if you can show any subject matches the definitions, all the remaining results hold, whether the system is a gas, an economy, or a painting. Ruelle mentions early that this has been done in constructive quantum field theory and differential dynamical systems. There is no physics in the work, except to try to explain the symbols. It reads rather annoyingly like a poorly written homework set by an extremely clever graduate student.
That said, when you’ve figured out what’s going on it’s an rewarding book. This completely formal approach does give a complimentary perspective on the topics covered. In the end, though, this is a book on Gibbs ensembles and classical thermodynamics, not on Fermi or Bose quantum systems. I do not know what would be required to incorporate those, and how many results will still hold when the probability measures are changed.
Appendix B, Open Problems, presents topics that were unsolved at the time of publication of the first edition (of 1976) at least one for every chapter after the first, and Appendix D is an update for the second edition. This is a very nice touch. There are also simple problems at the end of every chapter so you can figure out how little you understand before you move on to the next chapter.
I work in (experimental) solid state physics and have some (not much) scholastic background in applied analysis at the graduate level, and still I had to spend an afternoon trying to figure out what the symbols meant (that is, how x|L should be read, not what it corresponded to in real life; that was step two of three). The book didn’t get any easier. As interesting as the book is, I have to warn anyone without a very strong mathematical background away from this book, at least until he’s worked through an analysis text of some kind.
Summary: Detailed, advanced and complete treatment.
Rating: 4
Thermodynamic formalism is an area of mathematics developed to describe physical systems with a large number of components. A combination of advanced physics and mathematics, it is used to describe dynamic systems moving towards equilibrium and quantum mechanics applied to systems. The level of this book is advanced, generally the material would only be suitable for students at the graduate level. Exercises are given at the end of each chapter, although solutions are not provided. Additional background material on the necessary physics is included in a series of appendices.
The treatment of thermodynamic formalism is brief, detailed and complete. I strongly recommend the book as a textbook or study aid in that area.
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