Unit name | Statistical Mechanics 34 |
---|---|
Unit code | MATHM4500 |
Credit points | 20 |
Level of study | M/7 |
Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
Unit director | Professor. Liverpool |
Open unit status | Not open |
Pre-requisites |
Mechanics 2 or 23 (MATH 21900 or 31910); not available to students who have done similar units in physics due to overlap. |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
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 of thermodynamis, 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 statisitcal assumptions are often justified, making a strongly predictive and irreversible theory from reversible mecanics. Mostly equilibrium situations will be covered, with a brief discussion of nonequilibrium and related numerical topics.
Aims
Introduction to the mathematical foundations of thermodynamics and statistical mechanics.
Syllabus
Thermodynamics
Equilibrium statistical mechanics
Dynamical foundations
Nonequilibrium statistical mechanics
Modern Topics
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 3 Mathematics unit MATH34300 Statistical Mechanics 3, sharing the lectures but with differentiated problems and exam.
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.
The final assessment mark for Statistical Mechanics 34 is constructed as follows:
Different homework assignments will be given out for the level 3 and M versions of this unit.
The exam for the level 3 and M versions of the unit will also be different.
See the unit homepage for advice.