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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

Thermodynamics

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

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

Scaling

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

Entropy

Derivation of Thermodynamics

Fluctuations

The Boltzmann Factor

Time’s Arrow

**Transport Phenomena**

Collisionless and Hydrodynamic Regimes

Maxwell’s Demon

Nonviscous Hydrodynamics

Sound Wave

Diffusion

Heat Conduction

Viscosity

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

**Noise**

Thermal Fluctuations

Nyquist Noise

Brownian Motion

Einstein’s Theory

Diffusion

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

Spin

Microcanonical Ensemble

Fermi Statistics

Bose Statistics

Determining the Parameters

Pressure

Entropy

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

Semiconductors

**The Bose Gas**

Photons

Bose Enhancement

Phonons

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

**Superfluidity**

Condensate Wave Function

Spontaneous Symmetry Breaking

Mean-Field Theory

Observation of Bose–Einstein Condensation

Quantum Phase Coherence

Superfluid Flow

Phonons: Goldstone Mode

**Superconductivity **

Meissner Effect

Magnetic Flux Quantum

Josephson Junction

DC Josephson Effect

AC Josephson Effect

Time-Dependent Vector Potential

The SQUID

Broken Symmetry

**Appendix**

**Index**

*Problems appear at the end of each chapter.*

### Biography

**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