Prerequisites

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Learning Outcomes and Assessment

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Synopsis

Introduction and revision of Thermodynamics:

The ideal gas; the van der Waals gas; equations of state; phase diagrams. Thermodynamic variables and potentials. Thermodynamic equilibrium in closed systems, maximum entropy; open systems and availability – relation to thermodynamic potentials and to the probability of a state.

Fundamentals of statistical mechanics:

Principle of equal equilibrium probability; microcanonical, canonical and grand canonical ensembles; partition function and grand partition function – relation to thermodynamic potentials and variables; maximisation of partition function. Paramagnetic salt in an external field; ensemble of simple harmonic oscillators.

Classical ideal gas:

Counting of states in the phase space; equipartition theorem; indistinguishability; ideal gas in the canonical ensemble; additional degrees of freedom and external potentials; chemical reactions and chemical equilibrium. Grand partition function; density series expansion; p-T ensemble; m-p-T ensemble; ideal gas in the grand canonical ensemble.

Quantum statistical mechanics:

Quantum to classical crossover; Bose-Einstein and Fermi-Dirac statistics; quantum states of an ideal gas. The ideal Fermi gas; low-temperature limit; entropy and heat capacity of fermions of at low temperatures. The ideal Bose gas; Bose-Einstein condensation. Black-body radiation, phonons and spin waves.

Classical interacting systems:

Liquids; radial distribution function; internal energy and equation of state; pair interaction and virial expansion; van der Waals equation of state revisited. Mixtures and mixing entropy; phase separation; phase diagrams and critical points. Phase transformations; symmetry breaking and order parameters; the Ising model; the Landau theory of phase transitions; 1st and 2nd order transitions, critical points and triple points; transitions in external fields; critical behaviour and universality.

Fluctuations and stochastic processes:

Fluctuations in thermodynamic variables; probability distribution of fluctuations; fluctuations at critical points. Thermal noise; Brownian motion; stochastic variables and Langevin equation; fluctuation-dissipation theorem. Probability distribution and simple diffusion; diffusion in external potentials; the Kramers problem; generalised diffusion equations.

BOOKS

Equilibrium Thermodynamics, Adkins (3rd edn CUP 1983).

Concepts in Thermal Physics, Blundell and Blundell (Oxford 2006)

Introductory Statistical Mechanics, Bowley & Sanchez  (Oxford 1996).

Statistical Physics (Course of Theoretical Physics, v.5), Landau & Lifshitz (Pergamon 1980)

Brownian Motion, Mazo (Oxford  2002)