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Statistical Mechanics in a Nutshell, by Luca Peliti
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Statistical mechanics is one of the most exciting areas of physics today, and it also has applications to subjects as diverse as economics, social behavior, algorithmic theory, and evolutionary biology. Statistical Mechanics in a Nutshell offers the most concise, self-contained introduction to this rapidly developing field. Requiring only a background in elementary calculus and elementary mechanics, this book starts with the basics, introduces the most important developments in classical statistical mechanics over the last thirty years, and guides readers to the very threshold of today's cutting-edge research.
Statistical Mechanics in a Nutshell zeroes in on the most relevant and promising advances in the field, including the theory of phase transitions, generalized Brownian motion and stochastic dynamics, the methods underlying Monte Carlo simulations, complex systems--and much, much more. The essential resource on the subject, this book is the most up-to-date and accessible introduction available for graduate students and advanced undergraduates seeking a succinct primer on the core ideas of statistical mechanics.
- Provides the most concise, self-contained introduction to statistical mechanics
- Focuses on the most promising advances, not complicated calculations
- Requires only elementary calculus and elementary mechanics
- Guides readers from the basics to the threshold of modern research
- Highlights the broad scope of applications of statistical mechanics
- Sales Rank: #1139023 in Books
- Published on: 2011-08-28
- Original language: English
- Number of items: 1
- Dimensions: 10.00" h x 1.10" w x 7.00" l, 2.30 pounds
- Binding: Hardcover
- 416 pages
Review
"Unlike typical textbooks . . . [Statistical Mechanics in a Nutshell] presents statistical mechanics as a more general theory with broader applications. . . . A graduate student or researcher who wants to explore the applications of statistical mechanics would be very well served by this book."--Choice
"Peliti's Statistical Mechanics in a Nutshell is a fantastic reference for those who know the subject, teach it, or need a quick technical reminder, especially on the topic of phase transitions, which are consistently featured in modern-day discussions. . . . Statistical Mechanics in a Nutshell provides the more general overview, with topics such as the renormalization group method. It includes a good mix of fundamental thermodynamics, phase behaviour, and other key subjects."--Physics Today
From the Back Cover
"This book provides a clear, no-nonsense approach to the basic ideas of the subject as well as an introduction to some of its modern applications. The main ideas are well illustrated by examples and exercises. There are important sections on numerical methods and dynamics, and a final chapter on complex systems gives the reader a foretaste of current research. The volume will serve as an excellent introductory graduate text for students in physics, chemistry, and biology."--John Cardy, University of Oxford
"Statistical mechanics has seen an extraordinary broadening of application in recent decades, from economics and the social sciences to computer science and biology. Statistical Mechanics in a Nutshell combines in one accessible book the main classical ideas of statistical mechanics with many recent developments. It should have a wide readership among young (and also less young) scientists seeking a clear view of modern statistical physics."--Bernard Derrida, école Normale Supérieure
"This superb text provides a balanced and thorough treatment of statistical physics. From thermodynamics and basic principles to renormalization group, dynamics, and complex systems, the presentation is a model of clarity, and the level of detail is highly appropriate for graduate students or advanced undergraduates. Each chapter concludes with a helpful list of recommended further reading. I see this becoming a standard textbook for the next generation of PhD students."--Daniel Arovas, University of California, San Diego
"This is an excellent and comprehensive introduction to statistical mechanics in all of its aspects. The exposition is stimulating and concise but always clear, avoiding pedantic details. Statistical Mechanics in a Nutshell has the potential to become a standard reference."--Giovanni Gallavotti, Sapienza University of Rome
About the Author
Luca Peliti is professor of statistical mechanics at the University of Naples Federico II in Italy. His books include "Biologically Inspired Physics".
Most helpful customer reviews
22 of 24 people found the following review helpful.
Elementary And Advanced Text
By G. A. Schoenagel
A fine text from the Princeton Series, " In a Nutshell " .
First, an excerpt from the review in Journal of Statistical Physics (Ben-Avraham, 2012) :
"...remarkably self-contained and comprehensive introductory textbook..."
The Preface: author's stated goal: "..to be both a beginner's and advanced course."
The first five chapters are tailored for the beginner, the remainder decidedly more advanced.
The later chapters are largely independent of each other.
Next, my impressions:
Students should first read Appendices A, B & C : Legendre Transformations, Saddle Point Methods, Probability.
If the Appendices present no mathematical difficulty, then that encompassed between these covers should be accessible.
First (brief) Chapter, encompasses the Ideal Gas and derivation (via Maxwell's five postulates) of The Maxwell Distribution.
Next, Thermodynamics presented via a postulational (deductive) approach, and this clearly enunciated in 45-pages.
(Akin, in spirit, to Callen's more advanced tome). Exercise 2.2 (parts 1-8, Page 24) is not to be eschewed.
Take Note : Entropy as Extensive, Convex, Monotonic Function is elucidated to much effect in the remainder.
Statistical Mechanical fundamentals presented in the third chapter, lucidly expounding the basics:
phase space, observables, Louiville, quantum states, variational principle, Canonical and Grand Canonical Ensembles.
The Overarching Principle: Entropy in terms of accessible volume in Phase Space (Boltzmann).
Section 4.3.3 (Page 110) Variational derivation of Fermi and Bose Statistics, will entail student participation in working out
the manipulative details. That is, read along with paper and pencil to achieve any degree of competency with the text.
Chapter Five (Phase Transitions) is a delight; expressions derived for duality of Ising Model in two dimensions (Page 142),
Mean Fields supported via variational approach (Page 148) and exposition of Einstein's theory of fluctuations (Pages 157-160 ).
Chapter Five ends "the beginner's part". Later chapters (6-10) expound advanced material. In particular, I highlight:
Chapter Six (Renormalization Group) discussing connections between field theory and Einstein's theory of fluctuations.
Chapter Nine (Dynamics) surveys Brownian Motion and Stochastics, offering interplay between heuristic and analytical formalism.
A good supplement to Chapter Nine is the excellent, brief, An Introduction to Stochastic Processes, by Don Lemons (2002).
Scattered throughout we find in-line exercises (some merely manipulative, others asking for proofs--see Page 299, #9.1).
Also, recommended readings (especially important in order to supplement the brevity), culminating in a lengthy bibliography.
The exposition is terse, but lucid. Derivations generally straightforward to comprehend. (Chapter Six, probably the hardest).
While the back cover states "...requires only elementary calculus and elementary mechanics," it behooves the reader to
possess rather more background than this to fully digest the contents (see Page 243: Cauchy Residues, or, Dirac Delta).
An excellent Chapter Six, Renormalization Group, requires a bit more fluency in mathematical manipulation :
Cumulant Expansions, Differential Equations, Recurrence Relations; Page 206 , providing example of an involved derivation
of Equation 6.189 "...by passing to the Fourier transforms, we arrive at..." Integral Equations make entrance in Chapter Seven.
Another review notes, Physics Today (August 2012) :" It includes a good mix of fundamental thermodynamics, phase behavior,
and other key subjects. Even so, I do not see it as a standalone book for introductory students."
Thus, both elementary and advanced, this is a comprehensive textbook well worth consideration.
Highly Recommended.
0 of 0 people found the following review helpful.
Thus I can only recommend this book to someone who is highly experienced already ...
By Ian Hunter
Having read a number of statistical mechanics textbooks (Kardar stat of particles, Kardar stat of fields, Chandler, Pathria, and Huang), this ranks as one of the most problematic of all of them. At times it is extremely slow, but often skips lengthy parts of essential proofs. Thus I can only recommend this book to someone who is highly experienced already with the basics of thermo and stat mech. My largest pet peeve is that its notion is extremely inconsistent with existing literature. As a result I cannot even advise the use of it as a quick reference, as you have no idea whether F is helmholtz, or Gibbs, n is molarity of particle density, E is internal energy or total energy. At times this notation switches within a single problem.
That said it is functional, albeit with a large amount of work on the user side so I cannot give it a 1. I'd still recommend it over Huang and Pathria for info about Landau theory.
2 of 4 people found the following review helpful.
For math majors only
By Marsupial Tail
The text is good, until the author gets to the equations, at which point he totally loses the reader (me, at least). The author frequently skips steps in the equation derivations and expects the reader to follow while performing multi variate chain rule differentiation in his head. I have read many textbooks in mechanics and research in comp. chem and bio and the author still manages to lose me every two pages or so. Maybe this is good for geniuses, but for regulars maybe a more standard textbook like Atkins or Dill is better
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