Unit name | Statistical Mechanics |
---|---|

Unit code | MATH34300 |

Credit points | 20 |

Level of study | H/6 |

Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |

Unit director | Dr. Wiesner |

Open unit status | Not open |

Pre-requisites |
MATH11009 Mechanics 1 (or MATH10012 ODEs, Curves and Dynamics). Some of the concepts introduced in the course will be more familiar to those who have taken MATH21900 Mechanics 2 and MATH35500 Quantum Mechanics. From 2020/21, MATH21900 Mechanics 2 will be a pre-requisite. |

Co-requisites |
None |

School/department | School of Mathematics |

Faculty | Faculty of Science |

**Unit Aims**

Introduction to the mathematical foundations of thermodynamics and statistical mechanics.

**Unit Description**

The unit begins with a discussion of thermodynamics, the macroscopic (large scale) laws of heat. In contrast to mechanical systems, thermodynamics is fundamentally irreversible, so for example processes like thermal equilibration, combustion, and mixing can occur spontaneously, but the reverse processes never occur without external input. This leads to fixed constraints on the capabilities of (for example) engines, fridges and living organisms.

The remainder of the unit ("statistical mechanics") deals with the microscopic basis for thermodynamics, that is, explaining large scale properties from properties of individual molecules. Although the dynamical equations can be solved exactly in only a very few cases, the very large number of particles means that statistical assumptions are often justified, making a strongly predictive and irreversible theory from reversible mechanics. Both equilibrium and non-equilibrium situations will be covered, ending with a brief discussion of numerical simulation methods.

**Relation to Other Units**

Statistical mechanics is a branch of mathematical physics, along with mechanics, quantum mechanics and relativity. Its molecular treatment of fluids is complementary to the continuum approaches in the fluids units. There are also connections with information theory and chaotic dynamics. Connections with probability and statistics exist, but are not strong. Some parts of the unit are similar to Thermal Physics and Condensed Matter and Statistical Physics offered in physics; the approach here is more mathematical, and more directed towards research interests of the department, including fluids, dynamical systems, biological physics, nonequilibrium systems and computational methods.

Learning Objectives

By the end of the unit the students should be familiar with the main concepts of thermodynamics, equilibrium and nonequilibrium statistical mechanics, understand thermodynamic limitations of systems, and be able to derive thermodynamic properties of systems of weakly interacting particles.

Transferable Skills

Clear, logical thinking and an ability to comprehend and solve problems of mathematical physics.

A standard chalk-and-talk lecture unit of about 30 lectures, with occasional problems classes or informal discussion to meet the needs of individual students.

100% Examination.

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

**Recommended**

- C.J. Adkins,
*Equilibrium Thermodynamics,*Cambridge University Press, 1983 - David Chandler,
*Introduction to Modern Statistical Mechanics*, Oxford University Press, 1987 - J.R.Dorfman,
*An Introduction to Chaos in Non-equilibrium Statistical Mechanics*, Cambridge University Press, 1999 - Mehran Kardar,
*Statistical Physics of Particles*, Cambridge 2007 - Michel Le Bellac, Fabrice Mortessagne and G. George Batronni,
*Equilibrium and Non-equilibrium Statistical Thermodynamics*, Cambridge University Press, 2004 - R.K. Pathria,
*Statistical Mechanics*, Elsevier, 2005