Syllabus for Statistical Mechanics I

Other Useful Texts:

  • Molecular Driving Forces, by Sarina Bromberg and Ken A. Dill
  • Methods in Molecular Biophysics, by Igor N. Serdyuk, Nathan R. Zaccai and Joseph Zaccai
  • The principles of statistical mechanics, by Richard Chace Tolman, (QC 175.T584p)
  • Theory of Simple Liquids, by Jean-Pierre Hansen and Ian McDonald, (QC 145.2.H36 1986)
  • Understanding molecular simulation, by Daan Frenkel and Berend Smit, (QD 461 .F86 1996)
  • Computer Simulation of Liquids, by M.P. Allen and D.J. Tildesley, (QC 145.2.A43 1992)
  • Classical Mechanics, by Herbert Goldstein, (QA 805 .G6 1980)
  • A modern course in statistical physics, by L. E. Reichl, (QC 174.8.R44)
  • Statistical Mechanics, by Kerson Huang, (QC 174.8 .H83 1987)
  • Statistical Mechanics, by Shang-Keng Ma, (QC 174.8 .M2513 1985)
  • Mathematical Methods in the Physical Sciences, by Mary L. Boas, (QA 37.B662)
  • Statistical Mechanics: a Set of Lectures, by R.P. Feynman (QC 174.8 .F48)
  • Statistical thermodynamics of surfaces, interfaces, and membranes, by Samuel A. Safran, (QC 173.4 .S94 S24 1994)
  • Hydrodynamic fluctuations, broken symmetry, and correlation functions, by Dieter Forster, (QC 20.7 .C6 F67)
  • An Introduction to Statistical Thermodynamics, by Terrell L. Hill, (QC 20.7 .C6 F67)

Course Outline:

  1. Mathematical Review & Classical Mechanics (McQuarrie, Chapters 1-3 and Chandler, Chapter 3)
    1. Lagrangian Formulation
    2. Hamiltonian Formulation
    3. Poisson Brackets and Canonical Transformations
  2. Classical approach to Ensembles
    1. Ensembles and Phase Space
    2. Liouville's Theorem
    3. Equilibrium Statistical Mechanics and it's ensembles
  3. Elementary Probability Theory
    1. Distributions and Averages
    2. Cumulants and Fluctuations
    3. The Central Limit Theorem
  4. Distributions & Fluctuations (Chandler, Chapter 3)
    1. Theory of Ensembles, Classical and Quantum
    2. Equivalence of Ensembles
    3. Fluctuations of Macroscopic Observables
  5. Basic Thermodynamics (Chandler, Chapter 1)
    1. Review of Concepts
    2. The Laws of Thermodynamics
    3. Legendre Transforms
    4. The Maxwell Relations
    5. The Gibbs-Duhem Equation and Extensive Functions
    6. Intensive Functions
  6. Phases & Phase Transitions: The Ising Model (Chandler, Chapter 5)
    1. Stability of Thermodynamics Phases
    2. First-order Phase transitions
    3. Interfaces
    4. The Ising Model
    5. Lattice Gas
    6. Broken Symmetry
    7. Mean Field Theory
  7. Methodology (Chandler, Chapter 6)
    1. Monte Carlo
    2. Trajectories
    3. Non-Boltzmann Sampling
  8. A brief introduction to Liquid Theory (Chandler, Chapter 7 and McQuarrie, Chapter 13)
    1. Averages
    2. Distribution Functions
    3. Reversible Work Theorem
    4. g(r)
    5. Molecular liquids
  9. Non-equilibrium systems (Chandler, Chapter 8 and McQuarrie Chapters 19-21)
    1. Fluctuation-Dissipation Theorem
    2. Onsager's Regression Hypothesis
    3. Brownian Motion, Friction and the Langevin Equation
    4. Transport
    5. Time Correlation Functions