Undergraduate Course: Statistical Mechanics (PHYS09019)
Course Outline
School  School of Physics and Astronomy 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 9 (Year 3 Undergraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
Summary  This course provides an introduction to the microscopic formulation of thermal physics, generally known as statistical mechanics. We explore the general principles, from which emerge an understanding of the microscopic significance of entropy and temperature. We develop the machinery needed to form a practical tool linking microscopic models of manyparticle systems with measurable quantities. We consider a range of applications to simple models of crystalline solids, classical gases, quantum gases and blackbody radiation. 
Course description 
 Statistical description of manybody systems; formulation as a probability distribution over microstates; central limit theorem and macrostates.
 Statistical mechanical formulation of entropy.
 Minimisation of the free energy to find equilibrium.
 Derivation of the Boltzmann distribution from principle of equal a priori probabilities in extended system.
 Determination of free energy and macroscopic quantities from partition function; applications to simple systems (paramagnet, ideal gas, etc).
 Multiparticle systems: distinguishable and indistinguishable particles in a classical treatment; Entropy of mixing and the Gibbs paradox.
 FermiDirac distribution; application to thermal properties of electrons in metals.
 BoseEinstein distribution; application to the properties of black body radiation; BoseEinstein condensation.
 Introduction to phase transitions and spontaneous ordering from a statistical mechanical viewpoint: illustration of complexity arising from interactions; simpleminded meanfield treatment of an interacting system (e.g., van der Waals gas, Ising model); general formalism in terms of Landau free energy.
 Introduction to stochastic dynamics: need for a stochastic formulation of dynamics; principle of detailed balance; relaxation to equilibrium; application to Monte Carlo simulation; Langevin equation and random walks.

Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2022/23, Available to all students (SV1)

Quota: None 
Course Start 
Semester 2 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 22,
Summative Assessment Hours 8,
Revision Session Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
44 )

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework, 20%
Degree Examination, 80% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S2 (April/May)   2:00  
Learning Outcomes
On completion of this course a student should be able to:
1)define and discuss the concepts of microstate and macrostate of a model system
2)define and discuss the concepts and roles of entropy and free energy from the view point of statistical mechanics
3)define and discuss the Boltdsmann distribution and the role of the partition function
4)apply the machinery of statistical mechanics to the calculation of macroscopic properties resulting from microscopic models of magnetic and crystalline systems
5)discuss the concept and role of indistinguishability in the theory of gases; know the results expected from classical considerations and when these should be recovered
6)define the FermiDirac and BoseEinstein distributions; state where they are applicable; understand how they differ and show when they reduce to the Boltsman
distribution
7)apply the FermiDirac distribution to the calculation of thermal properties of elctrons in metals
8)apply the BoseEinstein distribution to the calculation of properties of black body radiation

Additional Information
Graduate Attributes and Skills 
Not entered 
Additional Class Delivery Information 
Workshop/tutorial sessions, as arranged. 
Keywords  StatM 
Contacts
Course organiser  Dr Alexander Morozov
Tel: (0131 6)50 5289
Email: alexander.morozov@ed.ac.uk 
Course secretary  Miss Emma Summers
Tel: (0131 6)51 7524
Email: esummer2@ed.ac.uk 

