Machine generated contents note: C.1. Heat Capacity. 1.1. What is Statistical Mechanics? -- 1.2. Probabilistic Behaviour -- 1.2.1. Axioms of Probability -- 1.2.2. Example: Coin Toss Experiment -- 1.2.3. Probability Distributions -- 1.2.4. Example: Random Walk -- 1.2.5. Large-Af Limit of the Binomial Distribution -- 1.2.6. Central Limit Theorem -- 1.3. Microstates and Macrostates -- 1.3.1. Example: Non-interacting Spins in a Solid -- 1.4. Information, Ignorance and Entropy -- 1.5. Summary -- Problems -- 2. The Microcanonical Ensemble -- 2.1. Thermal Contact -- 2.1.1. Heat Flow in the Approach to Equilibrium -- 2.1.2. Principle of Maximum Entropy -- 2.1.3. Energy Resolution and Entropy -- 2.2. Gibbs Entropy -- 2.3. Shannon Entropy -- 2.4. Example: Non-interacting Spins in a Solid -- 2.5. Summary -- Problems -- 3. Liouville's Theorem -- 3.1. Phase Space and Hamiltonian Dynamics -- 3.2. Ergodic Hypothesis -- 3.2.1. Non-ergodic Systems -- 3.3. Summary -- Problems -- 4. The Canonical Ensemble -- 4.1. Partition Function -- 4.2. Bridge Equation in the Canonical Ensemble -- 4.2.1. Boltzmann Distribution -- 4.2.2. Derivatives of the Partition Function -- 4.2.3. Equivalence of the Canonical and Microcanonical Ensembles -- 4.3. Connections to Thermodynamics -- 4.4. Examples -- 4.4.1. Two-Level System -- 4.4.2. Quantum Simple Harmonic Oscillator -- 4.4.3. Classical Partition Function and Classical Harmonic Oscillator -- 4.4.4. Rigid Rotor -- 4.4.5. Particle in a Box -- 4.5. Ideal Gas -- 4.5.1. Uncoupled Subsystems -- 4.5.2. Distinguishable and Indistinguishable Particles -- 4.5.3. Ideal Gas -- 4.5.4. Example: Entropy of Mixing -- 4.6. Non-ideal Gases -- 4.7. The Equipartition Theorem -- 4.7.1. Example: The Ideal Gas -- 4.7.2. Dulong and Petit Law -- 4.8. Summary -- Problems -- 5. Kinetic Theory -- 5.1. Maxwell-Boltzmann Velocity Distribution -- 5.1.1. Density of States -- 5.1.2. Maxwell-Boltzmann Velocity Distribution -- 5.2. Properties of the Maxwell-Boltzmann Velocity Distribution -- 5.2.1. Distribution of Speeds -- 5.3. Kinetic Theory for an Ideal Gas -- 5.3.1. Pressure in an Ideal Gas -- 5.3.2. Effusion -- 5.4. Brownian Motion -- 5.5. Diffusion -- 5.5.1. Mean Free Path and Collision Time -- 5.5.2. Fick's Law -- 5.6. Transport -- 5.7. Summary -- Problems -- 6. The Grand Canonical Ensemble -- 6.1. Chemical Potential -- 6.1.1. Example: Ideal Gas -- 6.2. Grand Canonical Partition Function -- 6.2.1. Bridge Equation -- 6.2.2. Derivatives of the Grand Potential -- 6.3. Examples -- 6.3.1. Fermions in a Two-Level System -- 6.3.2. The Langmuir Adsorption Isotherm -- 6.4. Chemical Equilibrium and the Law of Mass Action -- 6.4.1. The Law of Mass Action -- 6.5. Summary -- Problems -- 7. Quantum Statistical Mechanics -- 7.1. Quantum Statistics -- 7.2. Distinguishable Particles and Maxwell-Boltzmann Statistics -- 7.2.1. Maxwell-Boltzmann Statistics -- 7.3. Quantum Particles in the Grand Canonical Ensemble -- 7.3.1. Fermi-Dirac Distribution -- 7.3.2. Bose-Einstein Distribution -- 7.4. Density of States and Thermal Averages -- 7.4.1. Thermal Averages Using the Density of States -- 7.5. Summary -- Problems -- 8. Fermions -- 8.1. Chemical Potential for Fermions -- 8.1.1. Zero Temperature: The Fermi Energy -- 8.1.2. Non-zero Temperature: Sommerfeld Expansion -- 8.1.3. Temperature Dependence of the Chemical Potential -- 8.2. Thermodynamic Properties of a Fermi Gas -- 8.2.1. Energy and Heat Capacity -- 8.2.2. Pressure of a Fermi Gas -- 8.2.3. Entropy of a Fermi Gas -- 8.2.4. Number Fluctuations -- 8.2.5. Another View of Temperature Dependence of Thermodynamic Properties -- 8.3. Applications -- 8.3.1. Metals and the Fermi Sea -- 8.3.2. White Dwarf Stars -- 8.3.3. Neutron Stars -- 8.4. Summary -- Problems -- 9. Bosons -- 9.1. Photons and Blackbody Radiation -- 9.1.1. Blackbody Radiation -- 9.1.2. Density of States -- 9.1.3. Number Density -- 9.1.4. Energy Density -- 9.1.5. Example: Cosmic Microwave Background Radiation -- 9.1.6. Radiation Pressure -- 9.1.7. Stefan-Boltzmann Law -- 9.2. Bose-Einstein Condensation -- 9.2.1. Superfluidity -- 9.3. Low-Temperature Properties of a Bose Gas -- 9.3.1. Chemical Potential -- 9.3.2. Internal Energy and Heat Capacity -- 9.4. Bosonic Excitations: Phonons and Magnons -- 9.4.1. Phonons -- 9.4.2. The Debye Model -- 9.4.3. Magnons -- 9.5. Summary -- Problems -- 10. Phase Transitions and Order -- 10.1. Introduction to the Ising Model -- 10.2. Solution of the Ising Model -- 10.2.1. Order Parameters and Broken Symmetry -- 10.2.2. General Strategy for Solution of the Ising Model -- 10.2.3. Mean Field Theory -- 10.3. Role of Dimensionality -- 10.3.1. One Dimension -- 10.3.2. Two Dimensions -- 10.4. Exact Solutions of the Ising Model -- 10.4.1. Exact Solution in One Dimension -- 10.4.2. Exact Solution in Two Dimensions -- 10.5. Monte Carlo Simulation of the Ising Model -- 10.5.1. Importance Sampling -- 10.5.2. Metropolis Algorithm -- 10.5.3. Initial Conditions and Equilibration -- 10.6. Connection between the Ising Model and the Liquid-Gas Transition -- 10.7. Landau Theory -- 10.7.1. Symmetry-Breaking Fields -- 10.7.2. Landau Theory and First-Order Phase Transitions -- 10.8. Summary -- Problems -- Appendix A Gaussian Integrals and Stirling's Formula -- A.1. Gaussian Integrals -- A.2. Gamma Function -- A.3. Stirling's Formula -- Appendix B Primer on Thermal Physics -- B.1. Thermodynamic Equilibrium -- B.1.1. Reversible and Irreversible Processes -- B.1.2. State Functions -- B.1.3. Work and Heat -- B.2. The Laws of Thermodynamics -- B.3. Thermodynamic Potentials -- B.3.1. Legendre Transforms and Free Energies -- B.4. Maxwell Relations -- B.4.1. Useful Partial Derivative Relations -- B.4.2. Example: Relationship between Cy and Cp -- Appendix C Heat Capacity Cusp in Bose Systems -- C.1. Heat Capacity.
Summary:
"This clear and pedagogical text delivers a concise overview of classical and quantum statistical physics. Essential Statistical Physics shows students how to relate the macroscopic properties of physical systems to their microscopic degrees of freedom, preparing them for graduate courses in areas such as biophysics, condensed matter physics, atomic physics and statistical mechanics. Topics covered include the microcanonical, canonical, and grand canonical ensembles, Liouville's theorem, kinetic theory, non-interacting Fermi and Bose systems and phase transitions, and the Ising model. Detailed steps are given in mathematical derivations, allowing students to quickly develop a deep understanding of statistical techniques. End-of-chapter problems reinforce key concepts and introduce more advanced applications, and appendices provide a detailed review of thermodynamics and related mathematical results. This succinct book offers a fresh and intuitive approach to one of the most challenging topics in the core physics curriculum, and provides students with a solid foundation for tackling advanced topics in statistical mechanics"-- Provided by publisher.
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.