Class Topics
Tentative plan for the course:
Topic 1 - Postulates of classical thermodynamics, entropy, temperature, pressure, chemical potential
Topic 2 - Conditions for thermal, mechanical and chemical equilibrium; concavity of the entropy, the Euler relation, equations of state, the Gibb-Duhem relation, entropy of the ideal gas
Topic 3 - Energy minimum principle, Legendre transformations, Helmholtz free energy
Topic 4 - Enthalpy, Gibbs free energy, Grand Potential, heat reservoir, extrema principles for thermodynamic potentials, Maxwell's relations
Topic 5 - Response functions (specific heat, compressibility, thermal expansion) and relations between them, stability and curvature of free energies
Topic 6 - Kinetic theory of the ideal gas, Maxwell's velocity distribution, statistical ensembles and the ergodic hypothesis
Topic 7 - Liouville's theorem, microcanonical ensemble, density of states and number of states, connection to entropy
Topic 8 - Entropy of the ideal gas, entropy of mixing and Gibbs paradox, indistinguishable particles
Topic 9 - Canonical ensemble, energy fluctuations and specific heat, equivalence of microcanonical and canonical ensembles
Topic 10 - Average energy vs most probably energy, proof of Stirling's formula, factorization of canonical partition
function for non-interacting particles, ideal gas
Topic 11 - Virial and equipartition theorems, elastic vibrations of solids and the Law of Dulong and Petit, paramagnetism and the Curie Law
Topic 12 - Entropy and information theory
Topic 13 - The grand canonical ensemble, fluctuations of energy and number of particles
Topic 14 - The grand canonical partition function for non-interacting degrees of freedom, chemical equilibrium, absorption sites
Topic 15 - The density operator and quantum ensembles
Topic 16 - Quantum many particle systems, symmetry of the wavefunction, boson and fermions, non-interacting particles
Topic 17 - Two particle density matrix in real space, N particle partition function in real space representation, grand canonical partition function for non-interacting fermions and bosons
Topic 18 - Average occupation numbers, comparison with and validity of the classical limit of a quantum ideal gas, the harmonic oscillator and bosons
Topic 19 - Debye model for the specific heat due to ionic vibrations, black body radiation
Topic 20 - Ideal quantum gas of fermions or bosons, density, pressure, energy, classical limit
Topic 21 - Degenerate fermi gas, Sommerfeld model of electrons in a metal, Fermi energy, specific heat
Topic 22 - Pauli paramagnetism of an ideal fermi gas
Topic 23 - Ideal gas of bosons, Bose-Einstein condensation
Topic 24 - Bose-Einstein condensation in laser cooled atomic gases, classical spin models and ensembles
Topic 25 - Ising model, phase transitions and the thermodynamic limit, phase diagram
Topic 26 - Mean field approximation for the Ising model, graphical solution
Topic 27 - Critical exponents, Maxwell construction, Landau's theory of phase transitions
Topic 28 - Advanced topics