2nd Edition

Introduction to Statistical Physics

By Kerson Huang Copyright 2010
    334 Pages 137 B/W Illustrations
    by Chapman & Hall

    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.

    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

    The SQUID

    Broken Symmetry



    Problems appear at the end of each chapter.


    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