# Statistical Mechanics

Information for students taking the third-year 10-credit course Statistical Mechanics (the first half of the 20-credit module Statistical Mechanics and Solid State II) is now provided through the Yorkshare VLE

Indicative syllabus:

• Microstates: microstates (quantum states) and macrostates of a system, degeneracy W, density of states, illustration for a set of N harmonic oscillators, principle of equal equilibrium, probability of an isolated system, term “microcanonical ensemble”
• Thermal equilibrium, temperature: statistical nature of equilibrium illustrated for 2 systems of N harmonic oscillators, definition of temperature, Boltzmann distribution, partition function Z, term “canonical ensemble”
• Entropy: general statistical definition of entropy S, law of increase of entropy, entropy of isolated system in internal equilibrium (“microcanonical ensemble”), entropy of system in thermal equilibrium with a heat bath (“canonical ensemble”), Helmholtz free energy F; equivalence of classical and statistical entropy
• Elementary applications: Vacancies in solids; two-level systems (including magnetic susceptibility of dilute paramagnetic salt), simple harmonic oscillator (partition function, heat capacity).
• Vibrational heat capacity of solids: Quantisation of phonon modes, labelling of modes using wavevector; Einstein and Debye models
• Ideal gas: Partition function of monatomic gas, classical gas law, Maxwell-Boltzmann speed distribution, molecular gases (rotation and vibration), classical limit of occupation numbers
• Systems with variable number of particles: Grand canonical ensemble, chemical potential, Gibbs distribution
• Identical particles: Fermions and bosons, Fermi and Bose distributions, Bose-Einstein condensation, with applications to free-electron metals and nuclear physics (fermions), and liquid 4He and superconductivity (bosons)
• Black body radiation: Energy density, pressure
• The classical limit: Phase space, classical equipartition theorem