PX3249: Statistical Mechanics

School Cardiff School of Physics & Astronomy
Department Code PHYSX
Module Code PX3249
External Subject Code 100425
Number of Credits 10
Level L6
Language of Delivery English
Module Leader Professor David Jesson
Semester Spring Semester
Academic Year 2015/6

Outline Description of Module

To provide an understanding of the basics of information theory and its relation to statistical mechanics.

To establish the relation between statistical mechanics and thermodynamics.

To develop the ability to use statistical mechanics to solve and give insight into a wide range of physical problems ranging from condensed matter to astrophysics.

On completion of the module a student should be able to

Prove elementary theorems in information theory and show their relation to statistical physics.

Relate macroscopic thermodynamic properties to the underlying microscopic quantum mechanical energy levels.

Develop and use statistical mechanical partition functions for a system.

Apply statistical mechanical methods to model a number of classical and quantum systems.

Derive and apply Fermi-Dirac and Bose-Einstein statistics. (White dwarfs and neutron stars; give qualitative derivation of the Chandrasekhar limit. Superfluids, Bose-Einstein condensates.)

How the module will be delivered

Lectures 22 x 1 hr, Exercises.

Skills that will be practised and developed

Problem solving. Investigative skills. Mathematics. Analytical skills.

How the module will be assessed

Examination and Continuous Assessment

Assessment Breakdown

Type % Title Duration(hrs)
Exam - Spring Semester 80 Statistical Mechanics 2
Written Assessment 20 Statistical Mechanics N/A

Syllabus content

Introductory concepts: History of information theory (Nyquist, Hartley, Shannon, Jaynes). Description of microscopic states of a system. Quantum description. Probabilities of states. Relation to macroscopic ideas.

Thermodynamics and statistical mechanics: Conservation of Energy : thermodynamics and energy levels

Statistical Inference and information theory. Uncertainty. Bits, information transmission. Applications in communications.

Microcanonical, Canonical and Grand Canonical distributions, partition functions. Relation to thermodynamics. Bridge equations. Statistical interpretation of entropy and other thermodynamic variables. Fluctuations.

Applications: 2-level system, SHO, systems with independent modes. Application to models of solids : Einstein solid and coupled oscillators. Magnetic systems: Paramagnetism. (Ferromagnetism, Ising model).

Many Particles : Distinguishable and indistinguishable particles. Ideal Fermi and Bose gases. Degeneracy pressure. Chemical potential. Classical gas (Maxwell-Boltzmann).

Applications: Conduction electrons, Helium-4, Bose-Einstein condensates. Contact potential. Black body radiation. Equilibrium and stability of stars. Nonrelativistic and ultrarelativistic electrons. Masses and radii of white dwarfs, Chandrasekhar limit and its qualitative (Landau) derivation. Cooling of white dwarfs. Neutron stars, pulsars.

Background Reading and Resource List

Probability and Information, D Applebaum (Cambridge University Press).

Communications Systems, A B Carlson (McGraw-Hill).

Statistical Physics, F Mandl (Wiley).

Statistical Physics, L Landau and E Lifshitz (Addison-Wesley).

Thermal Physics, C Kittel and H Kroemer (Freeman).

Black Holes, White Dwarfs and Neutron Stars, S Shapiro and S Teukolsky (Wiley).


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