# Unit information: Statistical Mechanics 34 in 2015/16

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Unit name Statistical Mechanics 34 MATHM4500 20 M/7 Teaching Block 2 (weeks 13 - 24) Dr. Sieber Not open MATH 11009 Mechanics 1. However some of the concepts introduced in the course will be more familiar to those who have taken MATH21900 Mechanics 2 and MATH35500 Quantum Mechanics. None School of Mathematics Faculty of Science

## Description

Unit aims

Introduction to the mathematical foundations of thermodynamics and statistical mechanics.

General Description of the Unit

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 Mechanics 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.

This is a double-badged version of the Level 6 Mathematics unit MATH34300 Statistical Mechanics 3, sharing the lectures but with differentiated problems and exam.

Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/

## Intended learning outcomes

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.

## Teaching details

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.

## Assessment Details

80% Examination and 20% Coursework.

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.

## Reading and References

See the unit homepage for advice.

• Statistical Mechanics, R.K. Pathria, Elsevier 2005, 529 pages.
• Equilibrium Thermodynamics, C.J. Adkins, Cambridge 1983, 285 pages.
• Introduction to Modern Statistical Mechanics, D. Chandler, Oxford 1987, 274 pages.
• Equilibrium and non-equilibrium statistical thermodynamics, M. LeBellac, F. Mortessagne and George Batronni, Cambridge 2004, 616 pages.
• An introduction to chaos in non-equilibrium statistical mechanics , J.R.Doffman. Cambridge 1999, 287 pages.

Statistical Physics of Particles, M. Kardar, Cambridge 2007, 330 pages.