Synopsis for C6.2a: Statistical Mechanics

Level: M-level Method of Assessment: Written examination.
Weight: Half-unit. OSS paper code to follow.

Prerequisites

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

Overview

This course aims to provide an introduction to the tools of statistical mechanics, which are used to investigate collective behavior 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. More recently, ideas of statistical mechanics have given powerful results in areas of study such as social networks and finance.

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 some modern research topics in the field.

Synopsis

Thermodynamics and Probability (3 lectures): microscopic versus macroscopic viewpoints, the laws of thermodynamics, temperature, entropy, free energy, etc.

Classical Statistical Mechanics (4 lectures): ideal gas, Gibbs paradox, canonical and grand canonical ensembles, Liouville's theorem and ergodicity, Maxwell relations

Nonequilibrium Statistical Mechanics (2-3 lectures): Boltzmann equation, Boltzmann-Grad limit.

Phase Transitions (4 lectures): order parameters, phase transitions, critical phenomena, Ising model, Potts model, renormalization, symmetry breaking

Other Topics and Applications (2-3 lectures): This could vary from year to year, but a good example would be Bose-Einstein condensates or statistical mechanics of random graphs.

1. David Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press 1987)
2. M. Kardar, Statistical Physics of Particles (Cambridge University Press 2007)
3. M. Kardar, Statistical Physics of Fields (Cambridge University Press 2007)
4. F. Schwabl, Statistical Mechanics (Springer-Verlag 2002)
5. J.P. Sethna, Entropy, Order Parameters, and Complexity (Oxford University Press 2006) [available online at http://pages.physics.cornell.edu/sethna/StatMech/]