Boltzman: Boltzman








Physics 418: Statistical Mechanics I
Prof. S. Teitel ----- Spring 2002

Lecture Notes

My hand written class lecture notes are being scanned and uploaded for you to view. Please be warned that these are the notes I prepare for myself to lecture from - they are not in general carefully prepared for others to read. I make no guarentees about their legibility, or that they are totally free of errors. I hope, nevertheless that you will find them useful. The lectures are uploaded as pdf files, so you will need Adobe Acrobat Reader in order to read them. You can download Acrobat Reader for free here.

These lecture notes are also available online from the University Library's Voyager system. Just go to Voyager, click on "Search Voyager Catalogue", choose "Course Reserve", select "Teitel, S" from the instructor menu, and hit the "Search" button. On the resulting page, click on "Course notes [electronic]".

The lecture note files correspond roughly to the material presented in a given day's lecture. But you may on occassion find the end of one day's lecture at the start of the file for the next day's lecture, so please look there if you think there might be something missing.

  • Lecture 1 basic postulates of classical thermodynamics; extensive and intensive variables; maximum entropy principle and conditions for equilibrium

  • Lecture 2 concavity of entropy; Euler relation; Gibbs-Duhem relation; minimum energy principle (updated with minor corrections 2/21)

  • Lecture 3 Legendre transform and alternate thermodynamic potentials (Helmholtz and Gibbs free energies)

  • Lecture 4 Minimization principles for thermodynamic potentials, Maxwell relations, response functions (2nd derivatives)

  • Lecture 5 Stability of thermodynamic systems, kinetic theory of the ideal gas, ergodic hypothesis, ensemble averages (updated with minor corrections 2/21)

  • Lecture 6 Liouville's theorem, the microcanonical ensemble and its relation to the entropy, application to the ideal gas

  • Lecture 7 Entropy of mixing, indistinguishable particles, the canonical ensemble and partition function

  • Lecture 8 Helmholtz free energy and the canonical partition function, equivalence of canonical and microcanonical ensembles, non-interacting particles

  • Lecture 9 Virial and equipartition theorems, law of Dulong and Petit, Curie paramagnetism

  • Lecture 10 Entropy and information theory, grand canonical ensemble and grand canonical partition function

  • Lecture 11 Grand potential and grand canonical ensemble, fluctuations, non-interacting particles, ideal gas

  • Lecture 12 Quantum ensembles, density matrix, harmonic oscillator, Fermi-Dirac and Bose-Einstein symmetries of many particle systems

  • Lecture 13 Pauli exclusion principle, real space density matrix for two particles, quantum statistics and spatial correlations

  • Lecture 14 Fermi-Dirac and Bose-Einstein partition functions for non-interacting particles, occupation numbers, the classical limit, boson picture for harmonic oscillators, chemical equilibrium

  • Lecture 15 Debye model for the specific heat of a solid, black body radiation

  • Lecture 16 Fermi and Bose gases in the dilute limit - corrections to classical theory, degenerate Fermi gas - T=0 properties

  • Lecture 17 Degenerate Fermi gas, low temperature expansion and specific heat

  • Lecture 18 Pauli paramagnetism of the non-interacting electron gas

  • Lecture 19 Landau diamagnetism of the non-interacting electron gas

  • Lecture 20 Bose Einstein condensation in an ideal bose gas

  • Lecture 21 Bose Einstein condensation - specific heat and entropy

  • Lecture 22 Superfluid 4He, BEC in trapped atomic gases, classical gas with internal degrees of freedom

  • Lecture 23 Classical non-ideal gas - the Mayer cluster expansion

  • Lecture 24 Virial expansion for the equation of state, van der Waals theory of the liquid-gas phase transition

  • Lecture 25 Liquid-gas phase transition continued - Maxwell construction and coexistence curve

  • Lecture 26 Liquid-gas phase transition continued - behavior near the critical point, critical exponents; Clausius-Clapeyron relation and Gibbs sum rule

  • Lecture 27 The Ising model, magnetic ensembles, spontaneously broken symmetry, phase transitions and the thermodynamic limit

  • Lecture 28 The mean field solution of the Ising model and Landau's theory of 2nd order phase transitions

  • Lecture 29 Exact solution of the 1-d Ising model, Landau-Ginzburg theory and fluctuations about the mean field solution, the upper critical dimension

Last update: Monday, August 20, 2007 at 12:11:18 PM.