Gould H., Tobochnik J. Statistical and Thermal Physics: With Computer Applications

Princeton University Press, 2010. 411 p. — ISBN: 0691137447.This textbook carefully develops the main ideas and techniques of statistical and thermal physics and is intended for upper-level undergraduate courses. The authors each have more than thirty years' experience in teaching, curriculum development, and research in statistical and computational physicsStatistical and Thermal Physics begins with a qualitative discussion of the relation between the macroscopic and microscopic worlds and incorporates computer simulations throughout the book to provide concrete examples of important conceptual ideas. Unlike many contemporary texts on thermal physics, this book presents thermodynamic reasoning as an independent way of thinking about macroscopic systems. Probability concepts and techniques are introduced, including topics that are useful for understanding how probability and statistics are used. Magnetism and the Ising model are considered in greater depth than in most undergraduate texts, and ideal quantum gases are treated within a uniform framework. Advanced chapters on fluids and critical phenomena are appropriate for motivated undergraduates and beginning graduate students
ntegrates Monte Carlo and molecular dynamics simulations as well as other numerical techniques throughout the text
Provides self-contained introductions to thermodynamics and statistical mechanics
Discusses probability concepts and methods in detail
Contains ideas and methods from contemporary research
ncludes advanced chapters that provide a natural bridge to graduate study
Features more than 400 problems
Programs are open source and available in an executable cross-platform formatFromMicroscopic toMacroscopicBehaviorSome Qualitative Observations
Doing Work and the Quality of Energy
Some Simple Simulations
Measuring the Pressure and Temperature
Work, Heating, and the First Law of Thermodynamics
*The Fundamental Need for a Statistical Approach
*Time and Ensemble Averages
Models of Matter
The ideal gas
Interparticle potentials
Lattice models
Importance of Simulations
Dimensionless QuantitiesSupplementary Notes
Approach to equilibrium
Mathematics refresher
Vocabulary
Additional Problems
Suggestions for Further Reading
ThermodynamicConcepts
ntroduction
The System
Thermodynamic Equilibrium
Temperature
Pressure Equation of State
Some Thermodynamic Processes
Work
The First Law of Thermodynamics
Energy Equation of State
Heat Capacities and Enthalpy
Quasistatic Adiabatic Processes
The Second Law of Thermodynamics
The Thermodynamic Temperature
The Second Law and Heat Engines
Entropy Changes
Equivalence of Thermodynamic and Ideal Gas Scale Temperatures
The Thermodynamic Pressure
The Fundamental Thermodynamic Relation
The Entropy of an Ideal Classical Gas
The Third Law of Thermodynamics
Free Energies
Thermodynamic Derivatives
*Applications to Irreversible Processes
Joule or free expansion process
Joule-Thomson process
Supplementary Notes
The mathematics of thermodynamics
Thermodynamic potentials and Legendre transforms
Vocabulary
Additional Problems
Suggestions for Further Reading
Concepts ofProbability
Probability in Everyday Life
The Rules of Probability
Mean Values
The Meaning of Probability
Information and uncertainty
*Bayesian inference
Bernoulli Processes and the Binomial Distribution
Continuous Probability Distributions
The Central Limit Theorem (or Why Thermodynamics Is Possible)
*The Poisson Distribution or Should You Fly?
*Traffic Flow and the Exponential Distribution
*Are All Probability Distributions Gaussian?
*Supplementary Notes
Method of undetermined multipliers
Derivation of the central limit theorem
Vocabulary
Additional Problems
Suggestions for Further Reading
StatisticalMechanicsA Simple Example of a Thermal Interaction
Counting Microstates
Noninteracting spins
A particle in a one-dimensional box
One-dimensional harmonic oscillator
One particle in a two-dimensional box
One particle in a three-dimensional box
Two noninteracting identical particles and the semiclassical limit
The Number of States of Many Noninteracting Particles: Semiclassical Limit
The Microcanonical Ensemble (Fixed E, V , and N)
The Canonical Ensemble (Fixed T, V , and N)
Connection Between Thermodynamics and Statistical Mechanics in the Canonical Ensemble
Simple Applications of the Canonical Ensemble
An Ideal Thermometer
Simulation of the Microcanonical Ensemble
Simulation of the Canonical Ensemble
Grand Canonical Ensemble (Fixed T, V , and μ)
*Entropy is not a Measure of Disorder
Supplementary Notes
The volume of a hypersphere
Fluctuations in the canonical ensemble
Vocabulary
Additional Problems
Suggestions for Further Reading
MagneticSystems
Paramagnetism
Noninteracting Magnetic Moments
Thermodynamics of Magnetism
The Ising Model
The Ising Chain
Exact enumeration
Spin-spin correlation function
Simulations of the Ising chain
*Transfer matrix
Absence of a phase transition in one dimension
The Two-Dimensional Ising Model
Onsager solution
Computer simulation of the two-dimensional Ising model
Mean-Field Theory
*Phase diagram of the Ising model
*Simulation of the Density of States
*Lattice Gas
Supplementary Notes
The Heisenberg model of magnetism
Low temperature expansion
High temperature expansion
*Bethe approximation
Fully connected Ising model
Metastability and nucleation
Vocabulary
Additional Problems
Suggestions for Further Reading
Many-Particle Systems
The Ideal Gas in the Semiclassical Limit
Classical Statistical Mechanics
The equipartition theorem
The Maxwell velocity distribution
The Maxwell speed distribution
Occupation Numbers and Bose and Fermi Statistics
Distribution Functions of Ideal Bose and Fermi Gases
Single Particle Density of States
Photons
Nonrelativistic particles
The Equation of State of an Ideal Classical Gas: Application of the Grand Canonical Ensemble
Blackbody Radiation
The Ideal Fermi Gas
Ground state properties
Low temperature properties
The Heat Capacity of a Crystalline Solid
The Einstein model
Debye theory
The Ideal Bose Gas and Bose Condensation
Supplementary Notes
Fluctuations in the number of particles
Low temperature expansion of an ideal Fermi gas
Vocabulary
Additional Problems
Suggestions for Further Reading
TheChemicalPotential andPhaseEquilibria
Meaning of the chemical potential
Measuring the chemical potential in simulations
The Widom insertion method
The chemical demon algorithm
Phase Equilibria
Equilibrium conditions
Simple phase diagrams
Clausius-Clapeyron equation
The van der Waals Equation of State
Maxwell construction
*The van der Waals critical point
*Chemical Reactions
Vocabulary
Additional Problems
Suggestions for Further Reading
ClassicalGases andLiquidsDensity Expansion
The Second Virial Coefficient
*Diagrammatic Expansions
Cumulants
High temperature expansion
Density expansion
Higher order virial coefficients for hard spheres
The Radial Distribution Function
Perturbation Theory of Liquids
The van der Waals equation
*The Ornstein-Zernicke Equation and Integral Equations for g(r)
*One-Component Plasma
Supplementary Notes
The third virial coefficient for hard spheres
Definition of g(r) in terms of the local particle density
ray scattering and the static structure function
Vocabulary
Additional Problems
Suggestions for Further Reading
CriticalPhenomena
Landau Theory of Phase Transitions
Universality and Scaling Relations
A Geometrical Phase Transition
Renormalization Group Method for Percolation
The Renormalization Group Method and the One-Dimensional Ising Model
!The Renormalization Group Method and the Two-Dimensional Ising Model
Vocabulary
Additional Problems
Suggestions for Further Reading
A.1 Physical Constants and Conversion Factors
A.2 Hyperbolic Functions
A.3 Approximations
A.4 Euler-Maclaurin Formula
A.5 Gaussian Integrals
A.6 Stirling’s Approximation
A.7 Bernoulli Numbers
A.8 Probability Distributions
A.9 Fourier Transforms
A.10 The Delta Function
A.11 Convolution Integrals
A.12 Fermi and Bose Integrals