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Physics 418: Statistical Mechanics I
Prof. S. Teitel stte@pas.rochester.edu ----- Spring 2005

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.

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

• Lecture 3 - Legendre transform and alternate thermodynamic potentials: Helmholtz and Gibbs free energies, enthalpy, the grand potential

• Lecture 4 - reservoirs, minimum principle for free energies, Maxwell relations, response functions

• Lecture 5 - response functions: relations between them and conditions imposed by the requirements of thermodynamic stability

• Lecture 6 - kinetic theory of the ideal gas law, Maxwell's velocity distribution, statistical ensembles and the ergodic hypothesis

• Lecture 7 - Liouville's Theorem and equilibrium ensembles, density of states and number of states in the microcanonical ensemble

• Lecture 8 - number of states and entropy, the ideal gas, entropy of mixing and Gibbs' parodox

• Lecture 9 - indistinguishable particles, the canonical ensemble, the canonical partition function and the Helmholtz free energy

• Lecture 10 - energy fluctuations, equivalence of canonical and microcanonical ensembles, Stirling's formula, factorization of canonical partition function for non-interacting particles

• Lecture 11 - virial and equipartition theorems, thermal vibrations of crystals and the Law of Dulong and Petit, Curie paramagnetism

• Lecture 12 - entropy and information theory

• Lecture 13 - grand canonical ensemble, energy and particle fluctuations

• Lecture 14 - grand canonical partition function for non-interacting particles, chemical equilibrium, quantum ensembles

• Lecture 15 - quantum many particle systems, Bose-Einstein and Fermi-Dirac statistics

• Lecture 16 - two particle density matrix, grand partition function for non-interacting fermions and bosons

• Lecture 17 - average occupation numbers for bosons and fermions, the classical limit of quantum ensembles, harmonic oscillator vs. bosons

• Lecture 18 - Debye theory of the specific heat of solids, black body radiation

• Lecture 19 - ideal quantum gases, single particle density of states, the "standard" functions, quantum correction to the equation of state at low densities, degenerate Fermi gas at T=0

• Lecture 20 - degenerate Fermi gas: Sommerfeld expansion at low T, specific heat, Pauli paramagnetism

• Lecture 21 - Pauli paramagnetism continued, ideal bose gas and Bose-Einstein condensation

• Lecture 22 - thermodynamics of Bose-Einstein condensation, BEC in laser cooled atomic gases

• Lecture 23 - classical gas of molecules with internal degrees of freedom

• Lecture 24 - the classical non-ideal gas and the Mayer cluster expansion

• Lecture 25 - the virial expansion and the Van der Waals equation of state

• Lecture 26 - the Van der Waals theory of the liquid-gas phase transition

• Lecture 27 - the Van der Waals theory of the liquid-gas phase transition continued

• Lecture 28 - free energy along the coexistence curve, Clausisu-Clapeyron relation, Gibbs phase rule (notes combined with those of lecture 27)