Statistical Physics

Text:

L.E.Reichl, "A Modern Course in Statistical Physics", 2nd ed., Wiley, 1998.

Revised Mathematical Supplement


Part I.   Thermodynamics


Chapter 2: Introduction to Thermodynamics

Chap 2. Introduction to Thermodynamics       ( May 04, 2019 )     
  •    2.B. State Variables & Exact Differentials       ( Mar 21, 2019 )
  •    2.C. Some Mechanical Equations of State       ( Mar 23, 2019 )
  •    2.D. The Laws of Thermodynamics       ( Mar 28, 2019 )
  •    2.E. Fundamental Equation of Thermodynamics       ( Apr 01, 2019 )
  •     2.F. Thermodynamic Potentials
  •    2.F.0. Overview       ( May 04, 2019 )
  •    2.F.1. Internal Energy       ( Apr 15, 2019 )
  •    2.F.2. Enthalpy       ( Apr 07, 2019 )
  •    2.F.3. Helmholtz Free Energy       ( Apr 07, 2019 )
  •    2.F.4. Gibbs Free Energy       ( Apr 08, 2019 )
  •    2.F.5. Grand Potential       ( Apr 08, 2019 )
  •    2.F.6. Mnemonics       ( Apr 08, 2019 )
  •    2.G. Response Functions       ( Apr 10, 2019 )
  •     2.H. Stability of the Equilibrium State
  •    2.H.1. Conditions for Local Equilibrium in a PVT System       ( Apr 11, 2019 )
  •    2.H.2. Conditions for Local Stability in a PVT System       ( Apr 13, 2019 )
  •    2.H.3. Implications of the Stability Requirements for the Free Energies       ( Apr 14, 2019 )
  •    Zip file for Chap. 2       ( May 04, 2019 )

    Special Topics

    Chap 2. Special Topics       ( Apr 29, 2019 )     
  •    S2.A. Cooling & Liquefaction of Gases       ( Apr 18, 2019 )
  •    S2.B. Entropy of Mixing and the Gibbs Paradox       ( Apr 25, 2019 )
  •    S2.C. Osmotic Pressure in Dilute Solutions       ( Apr 21, 2019 )
  •     S2.D. The Thermodynamics of Chemical Reactions
  •    S2.D.1. The Affinity       ( Apr 27, 2019 )
  •    S2.D.2. Stability       ( Apr 28, 2019 )
  •    S2.E. The Thermodynamics of Electrolytes       ( Apr 29, 2019 )
  •    Zip file for Special Topics       ( Apr 29, 2019 )

    Chapter 3: Thermodynamics of Phase Transitions

  •    3.B. Coexistence Of Phases: Gibbs Phase Rule       ( May 02, 2019 )
  •    3.C. Classification of Phase Transitions       ( May 06, 2019 )
  •     3.D. Pure PVT Systems
  •    3.D.1. Phase Diagrams       ( May 09, 2019 )
  •    3.D.2. Coexistence Curves: Clausius-Clapyron Equation       ( May 12, 2019 )
  •    3.D.3. Liquid-Vapor Coexistence Region       ( May 22, 2019 )
  •    3.D.4. The van der Waals Equation       ( May 28, 2019 )
  •    Supplement: Properties of PVT Systems       ( Jun 03, 2019 )
  •    3.E._Superconductors       ( Jun 03, 2019 )
  •    3.F. The Helium Liquids       ( Jun 06, 2019 )
  •    3.G. Ginzburg-Landau Theory       ( Jun 17, 2019 )
  •    3.H. Critical Exponents       ( Jun 21, 2019 )
  •    Zip file for Chap. 3       ( Jun 24, 2019 )

    Special Topics

  •    S3.A. Surface Tension       ( Jun 27, 2019 )
  •    S3.B. Thermomechanical Effect       ( Jun 30, 2019 )
  •    S3.C. The Critical Exponents for the Curie Point       ( Jun 30, 2019 )
  •    S3.D. Tricritical Points       ( Jul 01, 2019 )
  •    S3.E. Binary Mixtures       ( Jul 11, 2019 )
  •    S3.F. The Ginzburg-Landau Theory of Superconductors       ( Jul 13, 2019 )
  •    Zip file for Special Topics       ( Jul 13, 2019 )

    Part II.   Concepts from Probability Theory


    Chapter 4: Elementary Probability Theory and Limit Theorems

  •    4.B. Permutations & Combinations       ( Jul 14, 2019 )
  •    4.C. Definition of Probability       ( Jul 15, 2019 )
  •     4.D. Stochastic Variables & Probability
  •    4.D.0. Introduction       ( Jul 18, 2019 )
  •    4.D.1. Distribution Functions       ( Jul 18, 2019 )
  •    4.D.2. Moments       ( Jul 18, 2019 )
  •    4.D.3. Characteristic Functions       ( Jul 18, 2019 )
  •    4.D.4. Jointly Distributed Stochastic Variables       ( Jul 21, 2019 )

  • Chapter 5: Stochastic Dynamics and Brownian Motion

  •    5.A. Introduction       ( Oct 25, 2017 )
  •    5.B. General Theory       ( Aug 12, 2018 )
  •    5.C. Markov Chains       ( May 26, 2018 )
  •    5.C.1. Spectral Properties       ( May 26, 2018 )
  •    5.C.2. Random Walk       ( May 22, 2018 )
  •     5.D. The Master Equation
  •    5.D.1. Derivation of the Master Equation       ( May 23, 2018 )
  •    5.D.2. Detailed Balance       ( May 23, 2018 )
  •    5.D.3. Mean First Passage Time       ( May 24, 2018 )
  •     5.E. Brownian Motion
  •    5.E.1. Langevin Equation       ( Nov 23, 2017 )
  •    5.E.2. The Spectral Density       ( May 24, 2018 )
  •    Zip file for Chap.5       ( Aug 12, 2018 )

    Special Topics

  •    S5.A. Time Periodic Markov Chain       ( Jun 04, 2018 )
  •     S5.B. Master Equation for Birth-Death Processes
  •    S5.B.1. The Master Equation       ( Jun 04, 2018 )
  •    S5.B.2. Linear Birth-Death Processes       ( Jun 02, 2018 )
  •    S5.B.3. Nonlinear Birth-Death Processes       ( Jun 03, 2018 )
  •     S5.C. The Fokker-Planck Equation
  •    S5.C.1. Probability Flow in Phase Space       ( Jun 04, 2018 )
  •    S5.C.2. Probability Flow for Brownian Particle       ( Jun 04, 2018 )
  •    S5.C.3. The Strong Friction Limit       ( Jun 03, 2018 )
  •    S5.C.4. Solution of Fokker-Planck Equations with One Variable       ( Jun 03, 2018 )
  •    S5.D. Approximations to the Master Equation       ( Jun 03, 2018 )
  •    Zip file for Special Topics       ( Jun 04, 2018 )

    Chapter 6: The Foundations of Statistical Mechanics

  •    6.B. The Classical Probability Density       ( Jun 05, 2018 )
  •    6.C. Ergodic Theory and the Foundations of Statistical Mechanics       ( Dec 20, 2017 )
  •    6.C.1. Examples       ( Jun 28, 2018 )
  •    6.D. The Quantum Probability Density Operator       ( Dec 27, 2017 )
  •    Zip file for Chap.6 (contains 'TwoBallsOnBoundedPlane.nb')       ( Jun 28, 2018 )

    Special Topics

  •    S6.A. Reduced Probability Densities and the BBGKY Hierarchy       ( Dec 29, 2017 )
  •    S6.B. Reduced Density Matrices and the Wigner Distribution       ( Jan 08, 2018 )
  •    S6.C. Microscopic Balance Equations       ( Jan 26, 2018 )
  •    S6.D. Mixing Flow       ( Jan 29, 2018 )
  •    S6.E. Anharmonic Oscillator Systems       ( Feb 27, 2018 )
  •    Zip file for Special Topics (contains 'WalkerFord.nb')       ( Feb 27, 2018 )

    Part III.   Equilibrium Statistical Mechanics


    Chapter 8: Order-Disorder Transitions and Renormalization Group

  •    8.B. Static Correlation Functions & Response Functions       ( Mar 01, 2018 )
  •    8.C. Scaling       ( Mar 09, 2018 )
  •    8.D. Microscopic Calculation of Critical Exponents       ( Apr 10, 2018 )
  •    Zip file for Chap.8 (contains 'block.nb')       ( Apr 10, 2018 )

    Special Topics

  •    S8.A. Critical Exponents for the S4 Model       ( Apr 30, 2018 )
  •    S8.A.1. Contributions from the Second Cumulant       ( Apr 30, 2018 )
  •    Zip file for Special Topics (contains 'graphs.nb')       ( Apr 30, 2018 )

    Chapter 9: Interacting Fluids

  •    9.B. Thermodynamics and the Radial Distribution Function       ( Apr 12, 2018 )
  •     9.C. Virial Expansion of the Equation of State
  •    9.C.1. Virial Expansion and Cluster Functions       ( May 01, 2018 )
  •    9.C.2. The Second Virial Coefficient       ( May 02, 2018 )
  •    9.C.3. Higher Order Virial Coefficients       ( May 03, 2018 )
  •    Zip file for Chap.9 (contains '9.C.*_Code.nb')       ( May 03, 2018 )

    Special Topics

  •    S9.A. The Pressure and Compressibility Equations       ( May 04, 2018 )
  •    S9.B. Ornstein-Zernicke Equation       ( May 12, 2018 )
  •    S9.C. Third Virial Coefficient       ( May 13, 2018 )
  •    S9.D. Virial Coefficients for Quantum Gases       ( May 18, 2018 )
  •    Zip file for Special Topics       ( May 18, 2018 )

    Part IV.   Non-Equilibrium Statistical Mechanics


    Chapter 10: Hydrodynamic Processes Near Equilibrium

        10.B. Navier-Stokes Hydrodynamic Equations
  •    10.B.1. Balance Equations       ( Oct 18, 2018 )
  •    Appendix A. Balance Equations       ( May 27, 2018 )
  •    10.B.2. Entropy Source & Entropy Current       ( Jul 08, 2018 )
  •    10.B.3. Transport Coefficients       ( Jan 24, 2019 )
  •     10.C. Linearized Hydrodynamic Equations
  •    10.C.1. Linearization of the Hydrodynamic Equations       ( Jul 15, 2018 )
  •    10.C.2. Transverse Hydrodynamic Modes       ( Jul 15, 2018 )
  •    10.C.3. Longitudinal Hydrodynamic Modes       ( Jul 16, 2018 )
  •     10.D. Dynamic Equilibrium Fluctuations & Transport Processes
  •    Time Reversal Symmetry       ( Aug 06, 2018 )
  •    10.D.1. Onsager's Relations       ( Sep 23, 2018 )
  •    10.D.2. Wiener-Khintchine Theorem       ( Aug 16, 2018 )
  •     10.E. Linear Response Theory & the Fluctuation-Dissipation Theory
  •    10.E.1. The Response Matrix       ( Aug 25, 2018 )
  •    10.E.2. Causality       ( Aug 25, 2018 )
  •    10.E.3. The Fluctuation-Dissipation Theorem       ( Oct 29, 2018 )
  •    10.E.4. Power Absorption       ( Aug 27, 2018 )
  •     10.F. Transport Properties of Mixtures
  •    10.F.1. Entropy Production in Multi-Component Systems       ( Sep 09, 2018 )
  •    10.F.2. Fick's Law for Diffusion       ( Sep 09, 2018 )
  •    10.F.3. Thermal Diffusion       ( Sep 09, 2018 )
  •    10.F.4. Electrical Conductivity & Diffusion in Fluids       ( Sep 08, 2018 )
  •    Zip file for Chap.10       ( Jan 24, 2019 )

    Special Topics

  •    S10.A. Onsager's Relations When a Magnetic Field is Present       ( Sep 13, 2018 )
  •    S10.B. Microscopic Linear Response Theory       ( Sep 16, 2018 )
  •    S10.C. Light Scattering       ( Sep 20, 2018 )
  •    S10.D. Thermoelectricity       ( Sep 25, 2018 )
  •    S10.E. Entropy Production in Discontinuous Systems       ( Sep 29, 2018 )
  •    S10.F. Stochastic Hydrodynamics       ( Oct 06, 2018 )
  •     S10.G. Long-Time Tails
  •    S10.G.1. Fluid Flow Around the Brownian Particle       ( Oct 10, 2018 )
  •    S10.G.2. Drag Force on the Brownian Particle       ( Oct 12, 2018 )
  •    S10.G.3. Velocity Autocorrelation Function       ( Oct 15, 2018 )
  •     S10.H. Superfluid Hydrodynamics
  •    S10.H.1. Superfluid Hydrodynamic Equations       ( Oct 22, 2018 )
  •    S10.H.2. Sound Modes       ( Oct 23, 2018 )
  •    S10.I. General Definition of Hydrodynamic Modes       ( Oct 29, 2018 )
  •    Zip file for Special Topics (contains 'graph.nb')       ( Oct 29, 2018 )

    Chapter 11: Transport Theory

        11.B. Elementary Transport Theory
  •    11.B.1. The Maxwell-Boltzmann Distribution       ( Oct 30, 2018 )
  •    11.B.2. The Mean Free Path       ( Oct 30, 2018 )
  •    11.B.3. The Collision Frequency       ( Nov 01, 2018 )
  •    11.B.4. Self-Diffusion       ( Nov 03, 2018 )
  •    11.B.5. The Coefficients of Viscosity and Thermal Conductivity       ( Nov 03, 2018 )
  •    11.B.6. The Rate of Reaction       ( Nov 04, 2018 )
  •    11.C. The Boltzmann Equation       ( Nov 05, 2018 )
  •           11.C.1. Two-Body Scattering
  •         11.C.1.1. Dynamics of the Scattering Process       ( Dec 23, 2018 )
  •         11.C.1.2. The Scattering Cross Section       ( Nov 18, 2018 )
  •       11.C.2. Derivation of the Boltzmann Equation       ( Dec 02, 2018 )
  •       11.C.3. Boltzmann's H Theorem       ( Dec 02, 2018 )
  •      11.D. Linearized Boltzmann & Lorentz-Boltzmann Equations
  •       11.D.1. Kinetic Equations for a Two-Component Gas       ( Dec 06, 2018 )
  •       11.D.2. Collision Operators       ( Dec 18, 2018 )
  •      11.E. Coefficiant of Self-Diffusion
  •       11.E.1. Derivation of the Diffusion Equation       ( Dec 07, 2018 )
  •       11.E.2. Eigen-frequencies of the Lorentz-Boltzmann Equation       ( Dec 16, 2018 )
  •      11.F. Coefficiants of Viscosity & Thermal Conductivity
  •       11.F.1. Derivation of the Hydrodynamic Equations       ( Dec 13, 2018 )
  •       11.F.2. Eigen-frequencies of the Boltzmann Equation       ( Dec 17, 2018 )
  •       11.F.3. Shear Viscosity and Thermal Conductivity       ( Dec 17, 2018 )
  •    11.G._ComputationOfTransportCoefficients       ( Dec 17, 2018 )
  •       11.G.1. Sonine Polynomials       ( Dec 17, 2018 )
  •       11.G.2._DiffusionCoefficient       ( Dec 24, 2018 )
  •       11.G.3. Thermal Conductivity       ( Dec 25, 2018 )
  •       11.G.4. Shear Viscosity       ( Dec 25, 2018 )
  •    Zip file with Mathematica code for Chap.11 (contains 'graphics.nb' & 'scattering.nb')       ( Nov 28, 2018 )

       Zip file for Chap.11       ( Dec 25, 2018 )

    Special Topics

  •    S11.A. Beyond the Boltzmann Equation       ( Jan 02, 2019 )

  • Chapter 12: Nonequilibrium Phase Transitions

  •    12.B. Nonquilibrium Stability Criteria       ( Jan 03, 2019 )
  •       12.B.1. Stability Conditions Near Equilibrium       ( Jan 12, 2019 )
  •       Appendix C. Stability of Solutions to Nonlinear Equations       ( Jan 10, 2019 )
  •      12.B.2. Stability Conditions Far from Equilibrium
  •         12.B.2.1. General Arguments       ( Jan 12, 2019 )
  •         12.B.2.2. Stability of Nonlinear Chemical Reactions       ( Jan 14, 2019 )
  •    12.C. The Schlogl Model       ( Jan 17, 2019 )
  •      12.D. The Brusselator
  •       12.D.1. TheBrusselator: A Nonlinear Chemical Model       ( Jan 18, 2019 )
  •       12.D.2. Boundary Conditions       ( Jan 24, 2019 )
  •       12.D.3. Linear Stability Analysis       ( Jan 23, 2019 )
  •      12.E. The Rayleigh-Benard Instability
  •       12.E.1. Hydrodynamic Equations and Boundary Conditions       ( Jan 27, 2019 )
  •       12.E.2. Linear Stability Analysis       ( Jan 28, 2019 )
  •    Zip file for Chap.12       ( Jan 28, 2019 )

    Special Topics

  •    S.12.A.1. Fluctuations in the Rayleigh-Benard System       ( Mar 18, 2019 )
  •    S12.A.2. Fluctuations in the Brusselator       ( Mar 18, 2019 )
  •    Zip file for Special Topics       ( Mar 18, 2019 )

    Older version & notes for other chapters can be found      here


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