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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, GibbsDuhem 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 noninteracting 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
 Lecture 16  Fluctuations of energy in the grand canonical ensemble, noninteracting particles, chemical equilibrium, a gas in equilibrium with a surface of absorption sites
 Lecture 17  A gas in equilibrium with a surface of absorption sites, quantum statistical ensembles, density matrix operator
 Lecture 18  Quantum microcanonical, canonical, and grand canonical ensembles, quantum harmonic osciallator at temperature T, BoseEinstein and FermiDirac statistics, Pauli exlusion principle, occupation number representation
 Lecture 19  Density matrix for two noninteracting particles, quantum correlations as an effective classical pair interaction, Nparticle partition function in the positionspace basis
 Lecture 20  Partition functions for noninteracting quantum and classical ideal gas in the occupation number representation, average occupation number, the classical vs quantum limits of the ideal gas
 Lecture 21  The quantized harmonic oscillator as bosons, the Debye model for the specific heat of a solid
 Lecture 22  Black body radiation, the quantum ideal gas, standard functions, pressure, particle density, energy
 Lecture 23  Leading quantum correction to the ideal gas equation of state, the degenerate Fermi gas, Fermi energy, ground state energy, specific heat
 Lecture 24  Chemical potential of a degenerate Fermi gas at finite temperature, Pauli paramagnetism
Supplement: The Sommerfeld Expansion
 Lecture 25  The ideal Bose gas, BoseEinstein condensation in an ideal gas of free bosons
 Lecture 26  Classical spin models, constant magnetization vs constant magnetic field ensembles, broken symmetry and the possibility for a phase transition in the thermodynamic limit, Ising phase diagram
 Lecture 27  Meanfield solution of the Ising model, critical exponents
 Lecture 28  Meanfield solution and critical exponents continued, Maxwell construction, exact solution of the one dimensional Ising model

