Statistical Thermophysics [Facsimile] [Paperback]

Harry S. Robertson (Author)

Book Description

Publication Date: July 26, 1992 | ISBN-10: 0138456038 | ISBN-13: 978-0138456030 | Edition: 1

Based on the Gibbs maximum- entropy formalism, this statistical mechanics text offers the most direct, precise, and comprehensible foundation for the development of thermal physics, both macroscopic and statistical. Presenting a general entropy- maximizing variational principle for thermostatics and equilibrium statistical mechanics, the book also covers modern topics of phase transitions, critical phenomena, renormalization, interacting systems, and more. Of interest to physical chemists and professional physicists who need to update their reference libraries.

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From the Back Cover

Based on the Gibbs maximum- entropy formalism, this statistical mechanics text offers the most direct, precise, and comprehensible foundation for the development of thermal physics, both macroscopic and statistical. Presenting a general entropy- maximizing variational principle for thermostatics and equilibrium statistical mechanics, the book also covers modern topics of phase transitions, critical phenomena, renormalization, interacting systems, and more. Of interest to physical chemists and professional physicists who need to update their reference libraries.

Product Details

• Paperback: 592 pages
• Publisher: Prentice Hall; 1 edition (July 26, 1992)
• Language: English
• ISBN-10: 0138456038
• ISBN-13: 978-0138456030
• Product Dimensions: 9.2 x 7.5 x 1.2 inches
• Shipping Weight: 2 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,502,517 in Books (See Top 100 in Books)

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7 of 7 people found the following review helpful:

4.0 out of 5 stars Good book from the standpoint of information theory, September 5, 2001

By 

Dr. Lee D. Carlson (Baltimore, Maryland USA) - See all my reviews
(VINE VOICE)    (HALL OF FAME REVIEWER)    (REAL NAME)   

This review is from: Statistical Thermophysics (Paperback)

Statistical physics, mostly from the viewpoint of information theory, is the subject of this book, with the author freely admitting his intent to follow the work of Gibbs, Callen, Jaynes, and others in laying the foundations of the subject, and not that of Boltzmann. Without space to debate this approach here, what will be done is to emphasize the unique features of the book that have proven interesting or useful for study.

Appropriately, the book begins with a discussion of probability theory and its connection with information theory. The assignment of probabilities to a set of events is taken to represent information. The Shannon information entropy is derived and its role as a measure of uncertainty discussed. By maximizing the uncertainty subject to the usual constraints that the probabilities add to one and the equation for the mean value, the partition function is derived. Several examples are given to illustrate the time evolution of the probabilities and the approach to equilibrium. The examples also illustrate the evolution of the probabilities to a time-independent set that maximizes the uncertainty. An example of coupled harmonic oscillators is given to illustrate the approach to equilibrium, the equipartition of energy, and the evolution of the uncertainty to a value determined by the heat bath. The author is very detailed in this example, and he does not hestitate to use advanced mathematics when necessary. A highly interesting commentary on statistical physics is given at the end of the chapter.

A statistical models for thermostatics is developed in chapter 2 using the Shannon information entropy. The usual thermophysical relations are derived, and a thorough treatment of equilibrium thermodynamics is given, including the Maxwell relations. Most importantly, the author discusses the stability of equilibrium. Nonideal gases, such as van der Waals, and more practical topics such as chemical equilibrium, are discussed briefly.

The derivation of the fundamental relations of macroscopic thermodynamics from microphysical principles, or equilibrium statistical thermodynamics, is the subject of chapter 3. The treatment is pretty standard, with microcanonical, canonical, and grand canonical systems all discussed, via the calculating of the partition function. The calculation of the partition function for the general ideal gas is done nicely, and the author again returns to chemical equilibria but here in the context of the chapter.

Fermi-Dirac and Bose-Einstein statistics are given an elegant presentation in chapter 4, with a discussion of white dwarfs and neutron stars included. The treatment of Bose-Einstein condensation is somewhat dated, given the current experimental results.

The thermodynamics of dielectric and magnetic systems is discussed in the next chapter. The author is careful to include only those terms in the Hamiltonian for these systems that are due to local fields. This is helpful since most treatments on this topic in the literature are a little confusing.

Chapter 6 gives a detailed overview of phase transtions. The author distinguishes between first and second order phase transitions and the Landau theory and critical exponents are discussed.

Interactions between particles are considered in chapter 7, with the Ising model leading off the discussion, and its solution tackled first using the mean-field approximation. The exact solution of the one-dimensional Ising model is given, showing its analyticity. The transfer-matrix method is discussed, which is nice considering its importance in the area of exactly solved models in statistical physics. Raising the dimension by one causes more difficulties mathematically, but the Ising model in two dimensions is treated nicely using combinatorial and dimer-pfaffian methods.

Of upmost importance in fundamental theories of physics, such as quantum field theory, renormalization is treated in chapter 8, beginning with spin systems and via the Wilson approach.

The theory of irreversible processes is the subject of chapter 9, with the Onsager theory given initial consideration. The author does not neglect the Boltzmann equation, and the use of the relaxation-time approximation in its study. The hydrodynamic equations are derived using the zeroth-order approximation. The Pauli master equation is discussed as an equation for the time evolution of probabilities from the Markov process point of view. Quantum statistical physics is introduced via the statistical operator. The approach is the same as that taken in quantum field theory. Information-theoretic approaches are brought in, one being time-dependent maximum entropy formalism.

The book ends with a study of fluctuations, such as the Brownian motion of a particle on a lattice and the Langevin equation. The discussion of spectral density and autocorrelation functions reads like one straight out of a book on signal processing. The author again discusses response theory, introduces superoperator techniques, and proves the Kramers-Kronig relations.