Module Identifier 
PHM1510 
Module Title 
STATISTICAL PHYSICS 
Academic Year 
2007/2008 
Coordinator 
Professor Keith Birkinshaw 
Semester 
Semester 1 
Other staff 
Professor L Grischuck (Cardiff) 
PreRequisite 
Successful Completion of Year 3 of the MPhys Scheme 
Course delivery 
Lecture  20 lectures 

Seminars / Tutorials  3 seminars / tutorials 
Assessment 
Assessment Type  Assessment Length/Details  Proportion 
Semester Exam  2 Hours  80% 
Semester Assessment  Aberystwyth Assessment. Coursework  Examples Class. Deadline: Week 4 of the Semester  10% 
Semester Assessment  Cardiff Assessment. Course Work  Examples Class. Deadline: Week 10 of the Semester  10% 
Supplementary Exam  2 Hours Supplementary exam  100% 

Learning outcomes
After taking this module students should be able to:
INFORMATION THEORY

Justify the use of log(p) as a definition of information

Calculate the entropy/uncertainty associated with a probability distribution

Apply the concept of entropy in an analysis of communication systems with and without noise

Analyse the performance of a 1D array of detectors and the information content of a mass spectrum peak in terms of information theory

Show the relationship between 'Information Theory Entropy' and 'Thermodynamic entropy'.
ASTROPHYSICAL APPLICATIONS

Derive and apply the hydrostatic equilibrium equation for sphericallysymmetric stars.

Distinguish between normal stars governed by the MaxwellBoltzmann law and degenerate stars governed by the laws of the FermiDirac statistics.

Be capable of formulating the condition of degeneracy of the stellar gas in terms of the participating physical parameters.

Derive the equation of state for degenerate nonrelativistic and relativistic electron gases using the FermiDirac distribution function.

Perform a qualitative derivation of the Chandrasekhar limit for masses of white dwarfs and neutron stars in terms of fundamental constants.

Use the statistical mechanics of solid bodies for evaluation of heat capacity and cooling times of white dwarfs.

Name, describe and explain in detail various phenomena in laboratory and cosmic physics which are governed by the universal laws of quantum statictical mechanics.
Brief description
This module will be taught jointly with the Department of Physics at Cardiff, using the University of Wales video network. It consists of two blocks of lectures covering different applications of statistical physics:
(a) Information Theory (Aberystwyth)
(b) Astrophysical applications (Cardiff)
Content
Information Theory:
Information  the relation to probability
The message, the bit, message transmission  source, channel, destination, channel capacity, noise
Entropy and information rate
Mutual information
The binary symmetric channel (BSC)
Application in Communications, Spectroscopy and Statistical Mechanics
Identical, indistinguishable Bose and Fermi particles
Astrophysical Applications:
Equilibrium and stability of stars. Gravitational forces and pressure gradients. Normal and degenerate stars.
Breakdown of MaxwellBoltzmann gas law. FermiDirac/BoseEinstein statistics. Equation of state for ideal Fermi gas.
White dwarfs. Simple equations of state. Nonrelativistic and ultrarelativistic electrons.
Masses and radii of white dwarfs. The Chandrasekhar limit. Qualitative derivation of the Chandrasekhar limit.
Statistical mechanics of solids and cooling of white dwarfs. Comparison with observations.
Neutron stars. Masses and radii of neutron stars. Pulsars. Observations.
Transferable skills
Example classes, Tutorials.
Reading Lists
s
** General Text
L.D. Landau and E.M. Lifshitz (1969) Statistical Physics
AddisonWesley,
Books
A.B. Carlson Communication Systems
McGrawHill 0071005609
Applebaum Probability and Information
C.U.P. 0521555280
F. Mandl Statistical Physics
Wiley
Shapiro and Teukolsky Black Holes, White Dwarfs and Neutron Stars
Wiley 0471873160
Notes
This module is at CQFW Level 7