# C5.3 Statistical Mechanics - Material for the year 2020-2021

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Familiarity with classical mechanics and probability. [No lecture prerequisites, so in particular the Classical Mechanics lectures from Part B7.1 are not required. Everything will be self-contained.]

16 lectures

### Assessment type:

- Written Examination

This course aims to provide an introduction to the tools of statistical mechanics, which are used to investigate collective behaviour in complex systems of interacting entities. The traditional use of statistical mechanics is to study large numbers of interacting particles when tracking all of them using Newton's laws becomes infeasible. One thus studies ensembles and examines their statistical properties, such as the temperature in a room versus the vibrations of each individual molecule in the room. Ideas of statistical mechanics have given powerful results in areas of study such as polymer science.

Students will have developed a sound knowledge and appreciation of some of the tools, concepts, and computations used in the study of statistical mechanics. They will also get some exposure to modern research topics in the field.

Thermodynamics and Probability: microscopic versus macroscopic viewpoints, the laws of thermodynamics, temperature, entropy, free energy, etc.

Classical Statistical Mechanics: ideal gas, canonical and grand canonical ensembles, Liouville's theorem and ergodicity

Nonequilibrium Statistical Mechanics: Boltzmann equation.

Phase Transitions: order parameters, phase transitions (abrupt and continuous)

Possible other topics and applications: Polymer modelling, Fokker-Planck equation

- J.P. Sethna,
*Entropy, Order Parameters, and Complexity*(Oxford University Press 2006) - F. Schwabl,
*Statistical Mechanics*(Springer-Verlag 2002) - David Chandler,
*Introduction to Modern Statistical Mechanics*(Oxford University Press 1987) - M. Kardar,
*Statistical Physics of Particles*(Cambridge University Press 2007) - M. Kardar,
*Statistical Physics of Fields*(Cambridge University Press 2007)