# Unit information: Statistical Mechanics in 2021/22

Unit name Statistical Mechanics MATH34300 20 H/6 Teaching Block 2 (weeks 13 - 24) Professor. Liverpool Not open MATH10012 ODEs, Curves and Dynamics, MATH21900 Mechanics 2 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 including Unit Aims

Lecturers: Tannie Liverpool and Nugzar Suramlishvili

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.

## 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 Information

The unit will be taught through a combination of

• synchronous online and, if subsequently possible, face-to-face lectures
• asynchronous online materials, including narrated presentations and worked examples
• guided asynchronous independent activities such as problem sheets and/or other exercises
• synchronous weekly group problem/example classes, workshops and/or tutorials
• synchronous weekly group tutorials
• synchronous weekly office hours

## Assessment Information

90% Timed, open-book examination 10% 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.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

## Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATH34300).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.