Introduction to Statistical Physics

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.

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

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.