Statistical mechanics
Summary
This course presents an introduction to statistical mechanics geared towards materials scientists. The concepts of macroscopic thermodynamics will be related to a microscopic picture and a statistical interpretation. Lectures and exercises will be complemented with hands-on simulation projects.
Content
- From macroscopic thermodynamics to statistical mechanics
- Probability: binomial distribution, central limit theorem, normal distribution
- Ensembles, observables and the partition function
- Examples from materials science
- Undistinguishable particles: Fermi and Bose-Einstein distributions
- Phase transitions: Ising model, spin glasses
- A brief introduction to renormalization group theory
- Theory of liquids - structure factor and radial distribution function
- Statistical theories of polymers
Keywords
thermodynamics, statistics, entropy, free energy
Learning Prerequisites
Important concepts to start the course
Phenomenological thermodynamics, probability and statistics. A brief "reminder" will be included at the beginning of the course. Practical exercises will be based on Mathematica notebooks: while they are structured in such a way that knowledge of Mathematica programming is not necessary, some familiarity with the software might be useful to go beyond the basic objectives of the exercises.
Learning Outcomes
By the end of the course, the student must be able to:
- Compute probabilities of correlated events
- Construct the partition function of simple model systems
- Compare thermodynamic concepts and the correspondent microscopic mechanisms
- Solve simple materials science problems using statistical tools
- Describe the statistical description of liquids and polymers
- Explain the meaning of renormalization group theory
- Conduct computer experiments using the provided simulation code
- Differentiate the meaning of different ensembles, and of the indistinguishability of quantum particles
Teaching methods
Ex cathedra, exercises, and guided simulation projects
Expected student activities
Students are expected to study demonstrations and fundamental concepts following the course slides and the reference books, to solve the problems given during the exercise sessions, and to prepare (in groups) reports for the computational laboratory activities.
Assessment methods
Continuous evaluation, graded lab reports, final oral exam
Resources
Bibliography
E. Fermi, Thermodynamics, Dover
D. Chandler, Introduction to Modern Statistical Mechanics, Oxford University Press
K. Huang, Statistical Mechanics
J. M. Yeomans, Statistical Mechanics of Phase Transitions
Ressources en bibliothèque
- Thermodynamics / Fermi
- Statistical Mechanics / Huang
- Statistical Mechanics of Phase Transitions / Yeomans
- Introduction to Modern Statistical Mechanics / Chandler
Notes/Handbook
Comprehensive lecture slides will be provided before each lecture
Moodle Link
In the programs
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Statistical mechanics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Lab: 1 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Statistical mechanics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Lab: 1 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Statistical mechanics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Lab: 1 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Statistical mechanics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Lab: 1 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Statistical mechanics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Lab: 1 Hour(s) per week x 14 weeks
- Type: optional