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Lecture Notes


PHY 418: Statistical Mechanics I
Prof. S. Teitel stte@pas.rochester.edu ---- Spring 2018

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 guarantees 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.

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 0 - Sketching the history of statistical mechanics and thermodynamics (another such page here.)

  • Lecture 1 - Postulates of classical thermodynamics, entropy, temperature, pressure, chemical potential

  • Lecture 2 - Conditions for thermal, mechanical and chemical equilibrium, concavity of the entropy, equations of state, Euler relation, Gibbs-Duhem relation

  • Lecture 3 - Entropy of the ideal gas, entropy maximum vs energy minimum principle, Legendre transformation

  • Lecture 4 - Legendre transformations, Helmholtz and Gibbs free energies, enthalpy, the grand potential, reservoirs, extremum principles for free energies

  • Lecture 5 - Maxwell relations, response functions and relations between them, stability constraints on response functions

  • Lecture 6 - Curvature of free energies and stability requirements for response functions, heat engines, thermodynamic efficiency, Carnot cycle

  • Lecture 7 - Kinetic theory of ideal gas, Maxwell velocity distribution, Ergodic hypothesis, statisitcal ensembles, density matrix

  • Lecture 8 - Liouville's theorem, microcanonical ensemble, density of states and connection to entropy

  • Lecture 9 - Entropy of the ideal gas and problem of extensivity, entropy of mixing and Gibbs paradox, indistinguishable particles

  • Lecture 10 - The canonical ensemble and the canonical partition function, Helholtz free energy and the canonical partition function, energy fluctuations, equivalence of canonical and microcanonical ensembles in the thermodynamic limit

  • Lecture 11 - Average energy vs most probably energy, Stirling's formula, factoring the canonical partition function for non-interacting objects, the ideal gas in the canonical ensemble

  • Lecture 12 - Maxwell velocity distribution revisited, the virial theorm, the equipartition theorem, elastic vibrations of a solid and the law of Dulong and Petit, paramagnetism of classical spins

  • Lecture 13 - The Curie law of paramagnetic susceptibility, a note about the proper choice of coordinates, entropy and information

  • Lecture 14 - Entropy and information, the grand canonical ensemble

  • Lecture 15 - The grand canonical partition function and the grand potential, fluctuations of the number of particles