Statistical Physics I: Equilibrium Statistical Mechanics (Springer Series in Solid-State Sciences) [Paperback]

Morikazu Toda (Author), Ryogo Kubo (Author), Nobuhiko Saito (Author), M. Toda (Translator), N. Saito (Translator)

Book Description

Publication Date: March 18, 2004 | ISBN-10: 3540536620 | ISBN-13: 978-3540536628 | Edition: 2nd

Statistical Physics I discusses the fundamentals of equilibrium statistical mechanics, focussing on basic physical aspects. No previous knowledge of thermodynamics or the molecular theory of gases is assumed. Illustrative examples based on simple materials and photon systems elucidate the central ideas and methods.

Editorial Reviews

Language Notes

Text: English (translation)
Original Language: Japanese

From the Back Cover

Statistical Physics I discusses the fundamentals of equilibrium statistical mechanics, focusing on basic physical aspects. No previous knowledge of thermodynamics or the molecular theory of gases is assumed. Illustrative examples based on simple materials and photon systems elucidate the central ideas and methods.

Product Details

• Paperback: 268 pages
• Publisher: Springer; 2nd edition (March 18, 2004)
• Language: English
• ISBN-10: 3540536620
• ISBN-13: 978-3540536628
• Product Dimensions: 9.1 x 6.1 x 0.7 inches
• Shipping Weight: 13.6 ounces (View shipping rates and policies)
• Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,545,403 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

3 of 3 people found the following review helpful:

5.0 out of 5 stars The best book on Statistical Mechanics, March 25, 2000

By A Customer

This review is from: Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer Series in Solid-State Sciences, 31) (Paperback)

Statistical Mechanics (1&2) by Toda and Kubo is the best textbook on statistical mechanics I've read. This book has some material such as Linear response theory(in vol 2), ergotic problems(in vol 1) which is difficult to find in other ones. I like the way the author write in linear response part. It is beautiful.

2 of 2 people found the following review helpful:

5.0 out of 5 stars The best book on Statistical Mechanics, March 26, 2000

By A Customer

This review is from: Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer Series in Solid-State Sciences, 31) (Paperback)

Statistical Mechanics (1&2) by Toda and Kubo is the best textbook on statistical mechanics I've read. This book has some material such as Linear response theory(in vol 2), ergotic problems(in vol 1) which is difficult to find in other ones. I like the way the author write in linear response part. It is beautiful.

8 of 9 people found the following review helpful:

4.0 out of 5 stars Good on stochastic processes, May 26, 2003

By 

Professor Joseph L. McCauley "Joseph L. McCauley" (Austria+Texas) - See all my reviews

This review is from: Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer Series in Solid-State Sciences, 31) (Paperback)

This text provides a good, readable introduction to Markov processes, including Fokker-Planck equations, from the standpoint of typical physical examples. A weakness is that (by only mentioning and not developing Ito calculus) the book does not make it clear to the reader that most stochastic processes are nonstationary. This is important: today, we are interested in far from equilibrium dynamics, much less so in dynamics near equilibrium where the fluctuation-dissipation theorem holds. On the other hand, the standard financial math texts (Baxter and Rennie, Steele, ...) do us no service in this direction either. The book goes beyond the older reference by Wax, which is still a very good introduction to Markov processes. In any case, no existing reference treats the general case of a space-time-dependent diffusion coefficient adequately, the case of most interest for the dynamics of financial markets. Now for details of the weak spots.

There are two mistakes on pages 65-68. The discussion is based on the sde dx=-R(x)dt+D(x,t)^1/2dB(t) where B(t) is a Wiener process. First, it is claimed that the random force D(x,t)^1/2dB is Gaussian with a white spectrum. In general, the random force is not even stationary unless D is independent of x. The unstated assumption is that the random force is always stationary, so that with R(x)<0 there is an approach to equilibrium. When the diffusion coefficient depends on x (or more generally on (x,t)) then there is no approach to equilibrium for the case of unbounded x even with R<0, as the lognormal model of standard finance theory so vividly shows. Second, even if an equilibrium solution of the corresponding Fokker-Planck equation 'exists', it cannot be reached dynamically when the force is nonstationary. Again, the lognormal model illustrates this point. Arguments (typical in economics) that an equilibrium solution 'exists' are meaningless are useless if the dynamics can't approach that solution.