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Statistical mechanics for beginners: a textbook for undergraduates
This textbook is for undergraduate students on a basic course in Statistical Mechanics. The prerequisite is thermodynamics. It begins with a study of three situations - the closed system and the systems in thermal contact with a reservoir - in order to formulate the important entropy from Boltzmann formula, partition function and grand partition function. Through the presentation of quantum statistics, Bose statistics and Fermi-Dirac statistics are established, including as a special case the classical situation of Maxell-Boltzmann statistics. A series of examples ensue the harmonic oscillator, the polymer chain, the two level system, bosons (photons, phonons, and the Bose-Einstein condensation) and fermions (electrons in metals and in semiconductors). A compact historical note on influential scientists forms the concluding chapter. The unique presentation starts off with the principles, elucidating the well-developed theory, and only thereafter the application of theory. Calculations on the main steps are detailed, leaving behind minimal gap. The author emphasizes with theory the link between the macroscopic world (thermodynamics) and the microscopic world.
178 pages, Paperback
First published August 19, 2010
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April 13, 2023
This is a rather strange book. That it has had only one edition is unsurprising.
First, somewhat irritatingly, the English used is rather poor. Either due to strange writing, or poor proofreading, small words (of, the, it...) are frequently omitted and while this does not usually obscure the meaning I found it a constant irritation.
The book takes a "postulate first" view of statistical mechanics, and so defines the principal results of statistical mechanics as postulates and then explores the consequences.
I prefer a different approach, where the statistics of assemblies of particles are shown to lead to
(1) at a statistical definition of temperature (as is now adopted by SI),
(2) identify at a statistical definition of entropy,
(3) identify the partition function,
(4) calculate the free energy function and
(5) therefore calculate all other thermodynamic quantities...
Benguigui's book starts by assuming all the above. It then explores some consequences, using a few examples (which are the standard examples).
The approach is very much based around thermodynamics, rather than statistical mechanics, and so assumes that students are fully comfortable with thermodynamics.
Potentials are defined and discussed before the idea of an ensemble is fully elucidated.
The first example using the microcanonical ensemble is for a system with just two energy states (the system is not specified), and therefore the calculation of the most probable microstate of the system is very simple, and is not immediately shown to be extendable to more complex situations.
The later chapters contain nicely worked full examples, but without a good foundation from the first chapters, I believe most students will struggle to use this book to arrive at an initial understanding.
In general, for a book at this level, I greatly prefer the book by A. Guenault: "Statistical Physics", which is more clearly written and appears to me to have a better pedagogical framework.
First, somewhat irritatingly, the English used is rather poor. Either due to strange writing, or poor proofreading, small words (of, the, it...) are frequently omitted and while this does not usually obscure the meaning I found it a constant irritation.
The book takes a "postulate first" view of statistical mechanics, and so defines the principal results of statistical mechanics as postulates and then explores the consequences.
I prefer a different approach, where the statistics of assemblies of particles are shown to lead to
(1) at a statistical definition of temperature (as is now adopted by SI),
(2) identify at a statistical definition of entropy,
(3) identify the partition function,
(4) calculate the free energy function and
(5) therefore calculate all other thermodynamic quantities...
Benguigui's book starts by assuming all the above. It then explores some consequences, using a few examples (which are the standard examples).
The approach is very much based around thermodynamics, rather than statistical mechanics, and so assumes that students are fully comfortable with thermodynamics.
Potentials are defined and discussed before the idea of an ensemble is fully elucidated.
The first example using the microcanonical ensemble is for a system with just two energy states (the system is not specified), and therefore the calculation of the most probable microstate of the system is very simple, and is not immediately shown to be extendable to more complex situations.
The later chapters contain nicely worked full examples, but without a good foundation from the first chapters, I believe most students will struggle to use this book to arrive at an initial understanding.
In general, for a book at this level, I greatly prefer the book by A. Guenault: "Statistical Physics", which is more clearly written and appears to me to have a better pedagogical framework.
Displaying 1 of 1 review