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Thermodynamics and Statistical Mechanics
- Author
- Daniel Arovas
- Publisher
- UC San Diego
- Source
- LibreTexts
- License
- CC BY-NC-SA
- Language
- EN
- Category
- Basic Sciences
Contents· 102 sections
- 01: Fundamentals of Probability
- 1.01: Statistical Properties of Random Walks
- 1.02: Basic Concepts in Probability Theory
- 1.03: Entropy and Probability
- 1.04: General Aspects of Probability Distributions
- 1.05: Bayesian Statistical Inference
- 1.S: Summary
- 02: Thermodynamics
- 2.01: What is Thermodynamics
- 2.02: The Zeroth Law of Thermodynamics
- 2.03: Mathematical Interlude - Exact and Inexact Differentials
- 2.04: The First Law of Thermodynamics
- 2.05: Heat Engines and the Second Law of Thermodynamics
- 2.06: The Entropy
- 2.07: Thermodynamic Potentials
- 2.08: Maxwell Relations
- 2.09: Equilibrium and Stability
- 2.10: Applications of Thermodynamics
- 2.11: Phase Transitions and Phase Equilibria
- 2.12: Entropy of Mixing and the Gibbs Paradox
- 2.13: Some Concepts in Thermochemistry
- 2.14: Appendix I- Integrating Factors
- 2.15: Appendix II- Legendre Transformations
- 2.16: Appendix III- Useful Mathematical Relations
- 2.S: Summary
- 03: Ergodicity and the Approach to Equilibrium
- 3.01: Modeling the Approach to Equilibrium
- 3.02: Phase Flows in Classical Mechanics
- 3.03: Irreversibility and Poincare Recurrence
- 3.04: Remarks on Ergodic Theory
- 3.05: Thermalization of Quantum Systems
- 3.06: Appendices
- 3.S: Summary
- 04: Statistical Ensembles
- 4.01: Microcanonical Ensemble (CE)
- 4.02: The Quantum Mechanical Trace
- 4.03: Thermal Equilibrium
- 4.04: Ordinary Canonical Ensemble (OCE)
- 4.05: Grand Canonical Ensemble (GCE)
- 4.06: Statistical Ensembles from Maximum Entropy
- 4.07: Ideal Gas Statistical Mechanics
- 4.08: Selected Examples
- 4.09: Statistical Mechanics of Molecular Gases
- 4.10: Appendix I- Additional Examples
- 4.S: Summary
- 05: Noninteracting Quantum Systems
- 5.01: Statistical Mechanics of Noninteracting Quantum Systems
- 5.02: Quantum Ideal Gases - Low Density Expansions
- 5.03: Entropy and Counting States
- 5.04: Lattice Vibrations - Einstein and Debye Models
- 5.05: Photon Statistics
- 5.06: The Ideal Bose Gas
- 5.07: The Ideal Fermi Gas
- 5.08: The Ideal Fermi Gas
- 5.09: Appendix I- Second Quantization
- 5.10: Appendix II- Ideal Bose Gas Condensation
- 5.11: Appendix III- Example Bose Condensation Problem
- 5.S: Summary
- 06: Classical Interacting Systems
- 6.01: Ising Model
- 6.02: Nonideal Classical Gases
- 6.03: Lee-Yang Theory
- 6.04: Liquid State Physics
- 6.05: Coulomb Systems - Plasmas and the Electron Gas
- 6.06: Polymers
- 6.07: Appendix I- Potts Model in One Dimension
- 6.S: Summary
- 07: Mean Field Theory of Phase Transitions
- 7.01: The van der Waals system
- 7.02: Fluids Magnets and the Ising Model
- 7.03: Mean Field Theory
- 7.04: Variational Density Matrix Method
- 7.05: Landau Theory of Phase Transitions
- 7.06: Mean Field Theory of Fluctuations
- 7.07: Global Symmetries
- 7.08: Ginzburg-Landau Theory
- 7.09: Appendix I- Equivalence of the Mean Field Descriptions
- 7.10: Appendix II- Additional Examples
- 7.S: Summary
- 08: Nonequilibrium Phenomena
- 8.01: Equilibrium Nonequilibrium and Local Equilibrium
- 8.02: Boltzmann Transport Theory
- 8.03: Weakly Inhomogeneous Gas
- 8.04: Relaxation Time Approximation
- 8.05: Diffusion and the Lorentz model
- 8.06: Linearized Boltzmann Equation
- 8.07: The Equations of Hydrodynamics
- 8.08: Nonequilibrium Quantum Transport
- 8.09: Stochastic Processes
- 8.10: Appendix I- Boltzmann Equation and Collisional Invariants
- 8.11: Appendix II- Distributions and Functionals
- 8.12: Appendix III- General Linear Autonomous Inhomogeneous ODEs
- 8.13: Appendix IV- Correlations in the Langevin formalism
- 8.14: Appendix V- Kramers-Kronig Relations
- 8.S: Summary
- 09: Renormalization
- 9.01: The Program of Renormalization
- 9.02: Real Space Renormalization
- 9.03: Block Spin Transformation
- 9.04: Scaling Variables
- 9.05: RSRG on Hierarchical Lattices The
- 9.S: Summary