Statistical Thermodynamics : Understanding the Properties of Macroscopic Systems book cover
1st Edition

Statistical Thermodynamics
Understanding the Properties of Macroscopic Systems

ISBN 9780367380762
Published September 5, 2019 by CRC Press
548 Pages 83 B/W Illustrations

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Book Description

Statistical thermodynamics and the related domains of statistical physics and quantum mechanics are very important in many fields of research, including plasmas, rarefied gas dynamics, nuclear systems, lasers, semiconductors, superconductivity, ortho- and para-hydrogen, liquid helium, and so on. Statistical Thermodynamics: Understanding the Properties of Macroscopic Systems provides a detailed overview of how to apply statistical principles to obtain the physical and thermodynamic properties of macroscopic systems.

Intended for physics, chemistry, and other science students at the graduate level, the book starts with fundamental principles of statistical physics, before diving into thermodynamics. Going further than many advanced textbooks, it includes Bose-Einstein, Fermi-Dirac statistics, and Lattice dynamics as well as applications in polaron theory, electronic gas in a magnetic field, thermodynamics of dielectrics, and magnetic materials in a magnetic field. The book concludes with an examination of statistical thermodynamics using functional integration and Feynman path integrals, and includes a wide range of problems with solutions that explain the theory.

Table of Contents

Basic Principles of Statistical Physics
Microscopic and Macroscopic Description of States
Basic Postulates
Gibbs Ergodic Assumption
Gibbsian Ensembles
Experimental Basis of Statistical Mechanics
Definition of Expectation Values
Ergodic Principle and Expectation Values
Properties of Distribution Function
Relative Fluctuation of an Additive Macroscopic Parameter
Liouville Theorem
Gibbs Microcanonical Ensemble
Microcanonical Distribution in Quantum Mechanics
Density Matrix
Density Matrix in Energy Representation

Thermodynamic Functions
Adiabatic Processes
Thermodynamic Identity
Laws of Thermodynamics
Thermodynamic Potentials, Maxwell Relations
Heat Capacity and Equation of State
Jacobian Method
Joule–Thomson Process
Maximum Work
Condition for Equilibrium and Stability in an Isolated System
Thermodynamic Inequalities
Third Law of Thermodynamics
Dependence of Thermodynamic Functions on Number of Particles
Equilibrium in an External Force Field

Canonical Distribution
Gibbs Canonical Distribution
Basic Formulas of Statistical Physics
Maxwell Distribution
Experimental Basis of Statistical Mechanics
Grand Canonical Distribution
Extremum of Canonical Distribution Function

Ideal Gases
Occupation Number
Boltzmann Distribution
Entropy of a Nonequilibrium Boltzmann Gas
Applications of Statistical Thermodynamics to Some Systems
Free Energy of the Ideal Boltzmann Gas
Equipartition Theorem
Monatomic Gas
Vibrations of Diatomic Molecules
Rotation of Diatomic Molecules
Nuclear Spin Effects
Electronic Angular Momentum Effect
Experiment and Statistical Ideas

Quantum Statistics of Ideal Gases
Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac Statistics
Generalized Thermodynamic Potential for a Quantum Ideal Gas
Fermi–Dirac and Bose–Einstein Distributions
Entropy of Nonequilibrium Fermi and Bose Gases
Thermodynamic Functions for Quantum Gases
Properties of Weakly Degenerate Quantum Gas
Degenerate Electronic Gas at Temperature Different from Zero
Experimental Basis of Statistical Mechanics
Application of Statistics to an Intrinsic Semiconductor
Application of Statistics to Extrinsic Semiconductor
Degenerate Bose Gas
Equilibrium or Black Body Radiation
Application of Statistical Thermodynamics to Electromagnetic Eigenmodes

The Electron Gas in a Magnetic Field
Evaluation of Diamagnetism of a Free Electron Gas; Density Matrix for a Free Electron Gas
Evaluation of Free Energy
Application to a Degenerate Gas
Evaluation of Contour Integrals
Diamagnetism of a Free Electron Gas; Oscillatory Effect

Magnetic and Dielectric Materials
Thermodynamics of Magnetic Materials in a Magnetic Field
Thermodynamics of Dielectric Materials in an Electric Field
Magnetic Effects in Materials
Adiabatic Cooling by Demagnetization

Lattice Dynamics
Periodic Functions of a Reciprocal Lattice
Reciprocal Lattice
Vibrational Modes of a Monatomic Lattice
Vibrational Modes of a Diatomic Linear Chain
Vibrational Modes in a Three-Dimensional Crystal
Normal Vibration of a Three-Dimensional Crystal

Condensed Bodies
Application of Statistical Thermodynamics to Phonons
Free Energy of Condensed Bodies in the Harmonic Approximation
Condensed Bodies at Low Temperatures
Condensed Bodies at High Temperatures
Debye Temperature Approximation
Volume Coefficient of Expansion
The Experimental Basis of Statistical Mechanics

Applications of Statistical Thermodynamics
Multiphase Systems
Critical Point

Macroscopic Quantum Effects: Superfluid Liquid Helium
Nature of the Lambda Transition
Properties of Liquid Helium
Landau Theory of Liquid He II
Superfluidity of Liquid Helium

Nonideal Classical Gases
Pair Interactions Approximation
Van Der Waals Equation
Completely Ionized Gas

Functional Integration in Statistical Physics
Feynman Path Integrals
Least Action Principle
Representation of Transition Amplitude through Functional Integration
Transition Amplitudes Using Stationary Phase Method
Representation of Matrix Element of Physical Operator through Functional Integral
Property of Path Integral Due to Events Occurring in Succession
Transition Amplitude for Time-Independent Hamiltonian
Eigenvectors and Energy Spectrum
Schrödinger Equation
Green Function for Schrödinger Equation
Functional Integration in Quantum Statistical Mechanics
Statistical Physics in Representation of Path Integrals
Partition Function of Forced Harmonic Oscillator
Feynman Variational Method
Feynman Polaron Energy



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Lukong Cornelius Fai is with ICTP Trieste, Italy and the University of Dschang, Cameroon. Gary Wysin is with Kansas State University, USA.


"... recommended for various levels of study: from a general course to the ground specialized course of theoretical physics. Moreover, a large number of problems based on physical situations supplied with detailed solutions determine an exceptional usefulness of this book due to the development of practical skills."
Zentralblatt MATH 1305