PH-616    Statistical Physics

  1. Intensive and extensive quantities, thermodynamic variables, thermodynamic limit, thermodynamic transformations.
  2. Classical ideal gas, first law of thermodynamics, application to magnetic systems, heat and entropy, Carnot cycle.
  3. Second law of thermodynamics, absolute temperature, temperature as integrating factor, entropy of ideal gas.
  4. Conditions for equilibrium, Helmholtz free energy, Gibbs potential, Maxwell relations, chemical potential. First-order phase transition, condition for phase coexistence.
  5. The statistical approach: phase space, distribution function, microcanonical ensemble, the most probable distribution, Lagrange multipliers.
  6. Maxwell-Boltzmann distribution: pressure of an ideal gas, equipartition of energy, entropy, relation to thermodynamics, fluctuations, Boltzmann factor.
  7. Transport phenomena: collisionless and hydrodynamic regimes, Maxwell’s demon, non-viscous hydrodynamics, sound waves, diffusion, conduction, viscosity.
  8. Quantum statistics: thermal wavelength, identical particles, Fermi and Bose statistics, pressure, entropy, free energy, equation of state, Fermi gas at low temperatures, application to electrons in solids and white dwarfs.
  9. The Bose gas: photons, phonons, Debye specific heat, Bose-Einstein condensation, equation of state, liquid helium.
  10. Canonical and grand canonical ensembles, partition function, connection with thermodynamics, fluctuations. minimization of free energy, photon fluctuations, pair creation.
  11. The order parameter, Broken symmetry, Ising spin model, Ginsburg – Landau theory, mean-field theory, critical exponents,  fluctuation-dissipation theorem, correlation length, universality.

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