Statistical Mechanics in a Nutshell by Luca Peliti (PDF)

Description

A concise introduction to statistical mechanicsStatistical 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 mechanicsFocuses on the most promising advances, not complicated calculationsRequires only elementary calculus and elementary mechanicsGuides readers from the basics to the threshold of modern researchHighlights the broad scope of applications of statistical mechanics

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Published in the Princeton series “… In a Nutshell,” this terse exposition really does present its content “in a nutshell. ” Read from one review: “remarkably self-contained and comprehensive introductory textbook (Ben-Avraham, Journal of Statistical Physics, 2012).” Read the preface: “… to be both a beginner’s and advanced course.” The initial five chapters are tailored for a beginner, the remainder tailored to a more advanced student. Later chapters are largely independent of each other. A few observations:(1) Read first appendices A, B, C: Legendre transformations, saddle point methods, and probability. If those appendices present little mathematical difficulty, the material between these covers should be accessible. Initial two chapters are brief and discuss ideal gas, plus derivation of Maxwell distribution (via Maxwell’s five postulates).(2) Thermodynamics is presented via a postulational (deductive) approach: enunciated in only 45-pages ! Akin, in spirit, to Callen’s beautiful tome. Exercise # 2.2 (parts 1-8, page 24) is not to be eschewed. Take note: Entropy as… extensive, convex, monotonic function… which is elucidated to much efficacy in the remainder.(3) Statistical mechanical foundation presented third chapter, lucidly expounding: phase space, observables, Liouville, quantum states, variational principle, canonical and grand canonical ensembles. The overarching principle: entropy in terms of accessible volume in phase space (ascribed to Boltzmann). Section 4.3.3 (page 110) is variational derivation of Fermi and Bose statistics, entailing student involvement in sorting out the manipulative details (you must read with paper and pencil in hand to achieve competency with the material). Chapter five, phase transitions, is a delight. Derive expressions for duality of the Ising model in two dimensions (page 142), mean fields by way of a variational approach and exposition of Einstein’s theory of fluctuations (page 148 and pages 157-160, respectively).(4) Chapter five concludes “the beginner’s part.” Following chapters (six through ten) are advanced. I highlight chapters six and nine. Six is renormalization group: beginning with Kadanoff (page 176), then one- and two- dimensional Ising model, followed by subtle mathematical manipulations. An easier chapter nine (dynamics) surveys Brownian motion and stochastics, offering an interplay between heuristic and analytical formalism. A supplement for chapter nine is the text: ” An Introduction to Stochastic Processes” (Lemons, 2002). The great book Atoms (Perrin, 1916) is recommended.(5) Scattered throughout are in-line exercises (some are merely manipulative, others ask only for a proof–for example, exercise #9.1, page 299). There is a “recommended readings list” (especially important in order to supplement brevity of the text), culminating in a lengthy bibliography. Exposition is terse but lucid. Derivations are straightforward. Renormalization group, chapter six, is the most difficult material here.(6) Back cover: “…requires only elementary calculus and elementary mechanics,” However, the reader needs to possess rather more background than that to fully assimilate contents (for instance, page 243: Cauchy residues or, Dirac delta). Also, the excellent chapter six, renormalization group, requires quite a lot more fluency in mathematical manipulation: cumulant expansions, differential equations, recurrence relations. Note one example of a challenging derivation: “…by passing to the Fourier transforms, we arrive at…” (equation 6.189, page 206). Integral equations make their entrance in chapter seven (classical fluids).(7) One reviewer: ” 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.” (Physics Today, August 2012). That may be correct ! This text is competitive with Chandler’s “Introduction to Modern Statistical Mechanics.” Salinas, Introduction to Statistical Physics (2001, Springer) is a fine companion to Peliti.

⭐An up to date and well written modern introduction to statistical mechanics. Suitable for advanced undergraduates or graduate students in the physical sciences or engineering. Easy to use for self-study or review.

⭐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.

⭐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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