This text developed from materials the author has used in a one-semester course on elementary statistical mechanics. It assumes readers have had courses in calculus and physical chemistry. Its purpose is not only to give students a deeper understanding of thermodynamics and the principles of equilibrium statistical mechanics, but also to introduce them to the modern topics of Monte Carlo sampling, renormalization group theory, and the fluctuation-dissipation theorem. By frequent use of simplified models, the author has kept the mathematics in the text relatively simple while presenting many of the sophisticated ideas in the field. His approach is to deal first with macroscopic thermodynamics, then with microscopic statistical principles. The Second Law of Thermodynamics appears as the direct consequence of the statistical assumption that microscopic equilibrium is the state of greatest randomness. The different ensembles and the role of fluctuations are treated before non-interacting ideal systems and phase transformations are discussed. The treatment of phase transitions relies on the Ising model, which is also used to explain the Monte Carlo method. The last two chapters deal with equilibrium statistical mechanics of classical fluids and with dynamics, that is, relaxation an molecular motion in macroscopic systems which are at or close to equilibrium. This is a forward-looking text suitable for use by advanced undergraduate or beginning graduate students of chemistry, biochemistry, chemical engineering and physics.
Show moreThis text developed from materials the author has used in a one-semester course on elementary statistical mechanics. It assumes readers have had courses in calculus and physical chemistry. Its purpose is not only to give students a deeper understanding of thermodynamics and the principles of equilibrium statistical mechanics, but also to introduce them to the modern topics of Monte Carlo sampling, renormalization group theory, and the fluctuation-dissipation theorem. By frequent use of simplified models, the author has kept the mathematics in the text relatively simple while presenting many of the sophisticated ideas in the field. His approach is to deal first with macroscopic thermodynamics, then with microscopic statistical principles. The Second Law of Thermodynamics appears as the direct consequence of the statistical assumption that microscopic equilibrium is the state of greatest randomness. The different ensembles and the role of fluctuations are treated before non-interacting ideal systems and phase transformations are discussed. The treatment of phase transitions relies on the Ising model, which is also used to explain the Monte Carlo method. The last two chapters deal with equilibrium statistical mechanics of classical fluids and with dynamics, that is, relaxation an molecular motion in macroscopic systems which are at or close to equilibrium. This is a forward-looking text suitable for use by advanced undergraduate or beginning graduate students of chemistry, biochemistry, chemical engineering and physics.
Show moreChapter 1: Thermodynamics, Fundamentals
First Law of Thermodynamics
Second Law
Variational Statement of Second Law
Application: Thermal Equilibrium and Temperature
Auxiliary Functions and Legendre Transforms
Maxwell Relations
Extensive Functions and the Gibbs-Duhem Equation
Intensive Functions
Chapter 2: Conditions for Equilibrium and Stability
Multiphase Equilibrium
Stability
Application to Phase Equilibria
Plane Interfaces
Chapter 3: Statistical Mechanics
The Statistical Method and Ensembles
Microcanonical Ensemble and the Rational Foundation of
Thermodynamics
Canonical Ensemble
A Simple Example
Generalized Ensembles and the Gibbs Entropy Formula
Fluctuations Involving Uncorrelated Particles
Alternative Development of Equilibrium Distribution Functions
Chapter 4: Non-Interacting (Ideal) Systems
Occupation Numbers
Photon Gas
Phonon Gas
Ideal Gases of Real Particles
Electrons in Metals
Classical Ideal Gases, the Classical Limit
Thermodynamics of an Ideal Gas of Structureless Classical
Particles
A Dilute Gas of Atoms
A Dilute Gas of Diatomic Molecules
Chemical Equilibria in Gases
Chapter 5: Statistical Mechanical Theory of Phase Transitions
Ising Model
Lattice Gas
Broken Symmetry and Range of Correlations
Mean Field Theory
Variational Treatment of Mean Field Theory
Renormalization Group (RG) Theory
RG Theory for the Two Dimensional Ising Model
Isomorphism Between Two-Level Quantum Mechanical System and the
Ising Model
Chapter 6: Monte Carlo Method in Statistical Mechanics
Trajectories
A Monte Carlo Trajectory
Non-Boltzmann Sampling
Quantum Monte Carlo
Chapter 7: Classical Fluids
Averages in Phase Space
Reduced Configurational Distribution Functions
Reversible Work Theorem
Thermodynamic Properties from g(r)
Measurement of g(r) by Diffraction
Solvation and Chemical Equilibrium in Liquids
Molecular Liquids
Monte Carlo for Hard Disks
Chapter 8: Statistical Mechanics of Non-Equilibrium Systems
Systems Close to Equilibrium
Onsager's Regression Hypothesis and Time Correlation Functions
Application: Chemical Kinetics
Another Application: Self Diffusion
Fluctuation Dissipation Theorem
Response Functions
Absorption
Friction and the Langevin Equation
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is an example of a text which requires a large degree of reader
participation. . . . People teaching modern statistical physics
will like the book and those who prefer a more traditional approach
will be pleasantly surprised to see a new way in which all
traditional subjects can be included in a textbook, so it can be a
valuable tool in teaching any course of statistical physics."
--Mathematical Reviews
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previous exposure to the subject. I strongly suspect that this book
will prove
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Education Supplement
"Exactly what I was looking for. I will also use this in my
graduate course."--Greg H. Zimmerman, Tennessee State
University
"An excellent introduction emphasizing major modern topics such as
Monte Carlo sampling, renormalization groups. and the
fluctuation-dissipation theorem." --American Mathematical
Monthly
"The text is clear and spare and addresses the latest developments
in statistical mechanics in a manner an undergraduate could readily
understand." --New Scientist
"A refreshing, lucid and much-needed textbook in an area which
remains inaccessible to many students."--G. P. Matthews, Plymouth
Polytechnic, England
"Chandler's book gives an excellent introduction to statistical
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physics or chemistry." --SIAM Review
"The book is highly recommended for the excellent discussions that
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"This is a book which pleases in many ways. The author's style is
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