Statistical Mechanics, spring 2017

Statistical Mechanics is a bachelor level Theoretical Physics course at the University of Helsinki, covering the basics of classical statistical physics. The most important aim of the course is to establish a link between the microscopic world of individual particles and macroscopic physical systems obeying the laws of thermodynamics. Topics covered during the course include the classical phase space, classical ensemble theory and equilibrium distributions, kinetic theory, as well as the basics of interacting systems.

Previous knowledge of classical mechanics and thermodynamics is assumed in the lectures. The students are also expected to comfortably master basic algebraic tools at the level of the courses Matemaattiset apuneuvot and Fysiikan matemaattiset menetelmät I.

The course is lectured in Finnish, but the homework problems are given in English. The lecture notes and course book are both in Finnish, but handwritten notes in English (from a previous year) as well as a list of international textbooks will be provided below.

NEW: Note that in period IV, the follow-up course Quantum Statistics will be lectured with the same weekly schedule.


Mondays 14.15-16.00 and Tuesdays 12.15-14.00 in E204. The first lecture takes place on January 16.

Lecturer: Aleksi Vuorinen, A322,

The course book is Statistinen fysiikka (J. Arponen and J. Honkonen, Limes ry, 2000). Additional recommended reading includes:


Fridays 14.15-16.00 in E205. The first exercise session is held on January 27.

Teaching Assistants: Francesco Montanari, A321, and Tuomas Tenkanen, A312,

The home work problem sets are published on this page on Tuesdays: Problem sets 1, 2, 3, 4, 5. Written solutions should be returned either directly to the lecturer or to his mailbox by the Tuesday of the following week. The solutions are graded, and they make up 1/4 of the final grade of the course.

Exam and results

The final exam will be held on Monday, March 6 at 9.00-13.00 in the lecture hall E204 of Physicum. The problems will be given both in Finnish and English, and it is ok to answer in either language.

The exam will cover all the material presented in the (Finnish) lecture notes as well as the chapters of the course book referred to in these notes. The lecture notes in English provided below cover almost all of this material, but the students are encouraged to check the Finnish lecture notes for individual items that might go beyond the English ones.

No "cheat sheets" are allowed in the exam, but a pocket calculator (not containing any stored material related to this class) is ok. All necessary lengthy formulas will be printed on the exam sheet.

The course results are now available here.

Timetable and lecture notes

The lectures followed the timetable given below, with the lecture notes linked to the corresponding week:

Week 1 (16.-17.1.): Reminder of classical mechanics, classical phase space
Week 2 (23-24.1.): Ensemble theory, the microcanonical and canonical ensembles
Week 3 (30.-31.1.): The grand canonical ensemble, fluctuations, basics of kinetic theory
Week 4 (6.-7.2.): Diffusion, Vlasov and Boltzmann equations, H theorem
No lectures on 13.-14.2. and no exercise session on 17.2
Week 5 (20.-21.2.): Maxwell-Boltzmann distribution, transport coefficients from the relaxation time approximation
Week 6 (27.-28.2.): Basics of interacting systems, review of course material
Week 7 (6.3.): Final exam at 9.00-13.00 in E204

Lecture notes from 2016, covering ~80% of the course material (in English):

Lecture 1 (Classical phase space)
Lecture 2 (Equilibrium distributions)
Lecture 2a (Grand canonical ensemble)
Lecture 2b (Ideal systems and summary)
Lecture 3 (Kinetic theory)
Lecture 3a (Maxwell-Boltzmann gas, relaxation time approximation)
Lecture 4 (Classical real gas)
Lecture 5 (More kinetic theory)