Course syllabus

TIF106 / FIM786: Non-equilibrium processes in physics, chemistry and biology

lp4 VT24 (7.5 hp)

The course is offered by the department of Physics.

Contact details

Examiner and lecturer: Johannes Hofmann, hofmannj@chalmers.se

TA: Enrique Rozas Garcia, enrique.rozas.garcia@physics.gu.se

Course purpose

The great majority of physical, chemical, and biological processes occur outside of thermodynamic equilibrium. How do we describe many-particle systems driven away from equilibrium, or evolving towards the equilibrium? In contrast to the universality of thermodynamics, the non-equilibrium evolution is system specific. The purpose of the course is to introduce basic concepts and practical tools to investigate non-equilibrium states. The course includes a selection of applications from physics, chemistry, and biology.

Schedule and Content

Schedule: TimeEdit

• Basic probability theory
• Fluctuations in physical systems
• Random walks and other stochastic processes
• Stochastic population dynamics, large-deviation theory
• Diffusion, Ornstein-Uhlenbeck process, fluctuation-dissipation theorem
• Langevin and Fokker-Planck equations
• First-passage times, Kramer's escape, transition-rate theory
• Reaction kinetics
• Kinetic theory for classical many-particle systems, Boltzmann equation, transport theory
• Hydrodynamics
• Models for particles in turbulence
• Brownian motors

Course literature

The main course material is presented in the lecture notes. For complementary reading, the following books are recommended:

• P. L. Krapivsky, S. Redner, E. Ben-Naim: A Kinetic View of Statistical Physics
• N. van Kampen: Stochastic Processes in Physics and Chemistry
• R. Livi, P. Politi: Nonequilibrium Statistical Physics: A Modern Perspective
• P. M. Chaikin, T.C. Lubensky, Principles of condensed matter physics (only last part of course)
• D. Arovas: Lecture Notes on Nonequilibrium Statistical Physics (A Work in Progress):
  https://courses.physics.ucsd.edu/2013/Fall/physics210b/LECTURES/STOCHASTIC.pdf

Course design

1. Lectures

The lectures present and discuss the main course material. The lecture notes will be made available on canvas (in the section "Modules/Lecture notes").

2. Exercise classes

The exercise classes discuss homework solutions and questions on the course material. It is important to attend the exercise classes and to prepare solutions to the exercises beforehand. Everyone is expected to participate in class and may be asked to present their solution.

3. OpenTA

Homework exercises are published on the OpenTA platform (section "OpenTA"). Some questions are marked as mandatory and will be graded. For these questions, a written solution must be uploaded via OpenTA (pdf of image upload) by the specified deadline.

4. Piazza

We use a Piazza forum for course discussions (section "Piazza"). You may have to sign up using your Chalmers or GU id if you have not used the platform before. You can post (and answer) questions as well as comments on the lectures and exercise classes.

5. Exam

The course will have a written exam on 29 May 2024. The exam contains five questions with five points each. 

You are allowed to bring one A4 page with handwritten notes (written on both sides) and a calculator. It is not allowed to bring lectures notes or course literature.

Changes made since the last occasion

2023: all lectures are joined now, no longer two tracks that divide kinetic theory and classical stochastic systems

Learning objectives and syllabus

Learning objectives:

After this course, the student should have acquired a general knowledge of stochastic processes and their use to describe the time evolution of systems in nature. More specifically, the student should be able to:

• understand basic concepts of probability theory and stochastic processes
• formulate diffusion models for stochastic physical, chemical, and biological systems
• solve Langevin and Fokker-Planck equations using standard mathematical and simulation methods
• give an overview over stochastic processes in physics, chemistry, and biology

Link to the syllabus on Studieportalen: Study plan

Examination form

To pass the course, you need to 

• Obtain a total of more than 50% of points in the graded homework solutions.
• Pass the exam (solve four out of five questions, with five points per question). Grade boundaries: CTH: ≥8 (3), ≥12 (4), ≥16 (5), GU: ≥8 (G), ≥14 (VG)

Homework solutions are only valid for this academic year. Students who fail the exam and the re-exam need to do the homework problems again next year.