C5.3 Statistical Mechanics (2021-22)

General Prerequisites:
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.]
Course Term: Hilary
Course Lecture Information: 16 lectures
Course Weight: 1
Course Level: M
Assessment Type: Written Examination
Course Overview:
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.
Learning Outcomes:
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.
Course Synopsis:
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