Introduction to Statistical Physics  book cover
2nd Edition

Introduction to Statistical Physics

ISBN 9781420079029
Published September 21, 2009 by Chapman and Hall/CRC
334 Pages 137 B/W Illustrations

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Book Description

Written by a world-renowned theoretical physicist, Introduction to Statistical Physics, Second Edition clarifies the properties of matter collectively in terms of the physical laws governing atomic motion. This second edition expands upon the original to include many additional exercises and more pedagogically oriented discussions that fully explain the concepts and applications.

The book first covers the classical ensembles of statistical mechanics and stochastic processes, including Brownian motion, probability theory, and the Fokker–Planck and Langevin equations. To illustrate the use of statistical methods beyond the theory of matter, the author discusses entropy in information theory, Brownian motion in the stock market, and the Monte Carlo method in computer simulations. The next several chapters emphasize the difference between quantum mechanics and classical mechanics—the quantum phase. Applications covered include Fermi statistics and semiconductors and Bose statistics and Bose–Einstein condensation. The book concludes with advanced topics, focusing on the Ginsburg–Landau theory of the order parameter and the special kind of quantum order found in superfluidity and superconductivity.

Assuming some background knowledge of classical and quantum physics, this textbook thoroughly familiarizes advanced undergraduate students with the different aspects of statistical physics. This updated edition continues to provide the tools needed to understand and work with random processes.

Table of Contents

A Macroscopic View of Matter

Viewing the World at Different Scales


The Thermodynamic Limit

Thermodynamic Transformations

Classic Ideal Gas

First Law of Thermodynamics

Magnetic Systems

Heat and Entropy

The Heat Equations

Applications to Ideal Gas

Carnot Cycle

Second Law of Thermodynamics

Absolute Temperature

Temperature as Integrating Factor


Entropy of Ideal Gas

The Limits of Thermodynamics

Using Thermodynamics

The Energy Equation

Some Measurable Coefficients

Entropy and Loss

TS Diagram

Condition for Equilibrium

Helmholtz Free Energy

Gibbs Potential

Maxwell Relations

Chemical Potential

Phase Transitions

First-Order Phase Transition

Condition for Phase Coexistence

Clapeyron Equation

Van der Waals Equation of State

Virial Expansion

Critical Point

Maxwell Construction


Nucleation and Spinodal Decomposition

The Statistical Approach

The Atomic View

Random Walk

Phase Space

Distribution Function

Ergodic Hypothesis

Statistical Ensemble

Microcanonical Ensemble

Correct Boltzmann Counting

Distribution Entropy: Boltzmann’s H

The Most Probable Distribution

Information Theory: Shannon Entropy

Maxwell–Boltzmann Distribution

Determining the Parameters

Pressure of Ideal Gas

Equipartition of Energy

Distribution of Speed


Derivation of Thermodynamics


The Boltzmann Factor

Time’s Arrow

Transport Phenomena

Collisionless and Hydrodynamic Regimes

Maxwell’s Demon

Nonviscous Hydrodynamics

Sound Wave


Heat Conduction


Navier–Stokes Equation

Canonical Ensemble

Review of the Microcanonical Ensemble

Classical Canonical Ensemble

The Partition Function

Connection with Thermodynamics

Energy Fluctuations

Minimization of Free Energy

Classical Ideal Gas

Grand Canonical Ensemble

The Particle Reservoir

Grand Partition Function

Number Fluctuations

Connection with Thermodynamics

Parametric Equation of State and Virial Expansion

Critical Fluctuations

Pair Creation


Thermal Fluctuations

Nyquist Noise

Brownian Motion

Einstein’s Theory


Einstein’s Relation

Molecular Reality

Fluctuation and Dissipation

Brownian Motion of the Stock Market

Stochastic Processes

Randomness and Probability

Binomial Distribution

Poisson Distribution

Gaussian Distribution

Central Limit Theorem

Shot Noise

Time-Series Analysis

Ensemble of Paths

Ensemble Average

Power Spectrum and Correlation Function

Signal and Noise

Transition Probabilities

Markov Process

Fokker–Planck Equation

The Monte Carlo Method

Simulation of the Ising Model

The Langevin Equation

The Equation and Solution

Energy Balance

Fluctuation-Dissipation Theorem

Diffusion Coefficient and Einstein’s Relation

Transition Probability: Fokker–Planck Equation

Heating by Stirring: Forced Oscillator in Medium

Quantum Statistics

Thermal Wavelength

Identical Particles

Occupation Numbers


Microcanonical Ensemble

Fermi Statistics

Bose Statistics

Determining the Parameters



Free Energy

Equation of State

Classical Limit

Quantum Ensembles

Incoherent Superposition of States

Density Matrix

Canonical Ensemble (Quantum-Mechanical)

Grand Canonical Ensemble (Quantum-Mechanical)

Occupation Number Fluctuations

Photon Bunching

The Fermi Gas

Fermi Energy

Ground State

Fermi Temperature

Low-Temperature Properties

Particles and Holes

Electrons in Solids


The Bose Gas


Bose Enhancement


Debye Specific Heat

Electronic Specific Heat

Conservation of Particle Number

Bose–Einstein Condensation

Macroscopic Occupation

The Condensate

Equation of State

Specific Heat

How a Phase Is Formed

Liquid Helium

The Order Parameter

The Essence of Phase Transitions

Ginsburg–Landau Theory

Relation to Microscopic Theory

Functional Integration and Differentiation

Second-Order Phase Transition

Mean-Field Theory

Critical Exponents

The Correlation Length

First-Order Phase Transition

Cahn–Hilliard Equation


Condensate Wave Function

Spontaneous Symmetry Breaking

Mean-Field Theory

Observation of Bose–Einstein Condensation

Quantum Phase Coherence

Superfluid Flow

Phonons: Goldstone Mode


Meissner Effect

Magnetic Flux Quantum

Josephson Junction

DC Josephson Effect

AC Josephson Effect

Time-Dependent Vector Potential


Broken Symmetry



Problems appear at the end of each chapter.

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Kerson Huang is Professor of Physics, Emeritus at MIT. Since retiring from active teaching, Dr. Huang has been engaged in biophysics research.


… suitable for advanced engineering study in an engineering or physics curriculum. … The problems at the end of each chapter and the discussion of applications will help students grasp many difficult concepts. … very readable and should be considered for an undergraduate program or by people wanting to learn about statistical physics.
IEEE Electrical Insulation Magazine, Vol. 27, No. 3, May/June 2011