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Illinois PHYS 466, Lecture 3: Basics of Statistical Mechanics

By David M. Ceperley

University of Illinois at Urbana-Champaign

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Basics of Statistical Mechanics

  • Review of ensembles
    • Microcanonical, canonical, Maxwell-Boltzmann
    • Constant pressure, temperature, volume,…
  • Thermodynamic limit
  • Ergodicity (see online notes also)
  • Reading assignment: Frenkel and Smit pgs. 1-22.


  • The Fundamentals according to Newton “Molecular Dynamics”
  • Statistical Ensembles
  • Environment
  • Interaction with environment: E= E1 + E2
  • Maxwell-Boltzmann Distribution
  • Thermodynamic limit
  • Ergodicity
  • Different aspects of Ergodicity
  • Particle in a smooth/rough circle
  • Fermi- Pasta- Ulam “experiment” (1954)
  • Distribution of normal modes
  • Distribution of normal modes vs time-steps
  • How do you judge if your results converged?
  • Continuum of dynamical methods with different dynamics and ensembles


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  • David M. Ceperley (2009), "Illinois PHYS 466, Lecture 3: Basics of Statistical Mechanics,"

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