Department of Physics, University of California, San Diego, 2013. — 440 p.Contents:
Preface
General references
Probability
References
A Statistical View
Probability Distributions from Maximum Entropy
General Aspects of Probability Distributions
Appendix : Bayesian Statistics
Thermodynamics
References
What is Thermodynamics?
The Zeroth Law of Thermodynamics
Mathematical Interlude : Exact and Inexact Differentials
The First Law of Thermodynamics
Heat Engines and the Second Law of Thermodynamics
The Entropy
Thermodynamic Potentials
Maxwell Relations
Equilibrium and Stability
Applications of Thermodynamics
Phase Transitions and Phase Equilibria
Entropy of Mixing and the Gibbs Paradox
Some Concepts in Thermochemistry
Appendix : Integrating factors
Appendix : Legendre Transformations
Appendix : Useful Mathematical Relations
Ergodicity and the Approach to Equilibrium
References
Modeling the Approach to Equilibrium
Phase Flows in Classical Mechanics
Irreversibility and Poincar´e Recurrence
Remarks on Ergodic Theory
Thermalization of Quantum Systems
Appendix : Formal Solution of the Master Equation
Appendix : Radioactive Decay
Appendix : Canonical Transformations in Hamiltonian Mechanics
Statistical Ensembles
References
Microcanonical Ensemble (μCE)
The Quantum Mechanical Trace
Thermal Equilibrium
Ordinary Canonical Ensemble (OCE)
Grand Canonical Ensemble (GCE)
Statistical Ensembles from Maximum Entropy
Ideal Gas Statistical Mechanics
Selected Examples
Statistical Mechanics of Molecular Gases
Appendix : Additional Examples
Noninteracting Quantum Systems
References
Statistical Mechanics of Noninteracting Quantum Systems
Quantum Ideal Gases : Low Density Expansions
Entropy and Counting States
Photon Statistics
Lattice Vibrations : Einstein and Debye Models
The Ideal Bose Gas
The Ideal Fermi Gas
Classical Interacting Systems
References
Ising Model
Nonideal Classical Gases
Lee-Yang Theory
Liquid State Physics
Coulomb Systems : Plasmas and the Electron Gas
Polymers
Appendix : Potts Model in One Dimension
Appendix : One-Particle Irreducible Clusters and the Virial Expansion
Mean Field Theory of Phase Transitions
References
The van derWaals system
Fluids, Magnets, and the Ising Model
Mean Field Theory
Variational Density Matrix Method
Landau Theory of Phase Transitions
Mean Field Theory of Fluctuations
Global Symmetries
Ginzburg-Landau Theory
Appendix : Equivalence of the Mean Field Descriptions
Appendix : Additional Examples
NonequilibriumPhenomena
References
Equilibrium, Nonequilibrium and Local Equilibrium
Boltzmann Transport Theory
Weakly Inhomogeneous Gas
Relaxation Time Approximation
Diffusion and the Lorentz model
Linearized Boltzmann Equation
The Equations of Hydrodynamics
Nonequilibrium Quantum Transport
Stochastic Processes
Appendix : Boltzmann Equation and Collisional Invariants
Appendix : Distributions and Functionals
Appendix : General Linear Autonomous Inhomogeneous ODEs
Appendix : Correlations in the Langevin formalism
Appendix : Kramers-Kronig Relations
