Non-equilibrium Statistical Physics

Course manual 2025/2026

Course content

Course Description 

In this course students will become familiar with fundamental classes of stochastic processes often encountered in many fields of physics. Starting from the most basic Brownian motion, we will derive/review/analyze the Fokker-Planck equation and formalism, linear response theory, fluctuation-dissipation relations, and several exotic classes of random walks that produce super- and sub- diffusive behavior. A particular focus will be devoted to scaling arguments, their construction and utility, and to concepts of universality. Examples from various fields of physics will be presented and discussed.  

Study materials

Literature

• Chaikin and Lubensky, 'Principles of condensed matter physics' 

• Pavel L. Krapivsky, Sidney Redner, and Eli Ben–Naim, 'A Kinetic View of Statistical Physics'. 

• J.-P. Bouchaud and A. Georges, Anomalous diffusion in disordered media, Phys. Rep. 195, 127 (1990).

•  Risken, H. 'The Fokker-Planck equation'

• Grigorios A. Pavliotis, 'Stochastic Processes and Application'.

Syllabus

• Langevin Theory of Brownian motion 

• Numerical integration of SDEs: the Euler–Maruyama method

• Brownian motion as a random walk and diffusion equation

• Generalized random walks and anomalous diffusion

• Kramers-Moyal expansion and Fokker-Planck equation

• Linear response theory and fluctuation-dissipation theorem

Practical training material

• Lecture notes, exercises and assignments  will be provided on Canvas.

Software

• python

Objectives

• Students will become familiar with a the most commonly encountered classes of statistical problems.
• Students will know how to describe stochastic processes, (in and out of equilibrium) either at the level of a Langevin equation (trajectories, SDE) and the level of a Fokker-Planck equation (distributions, PDE) and that the two are related.
• Students will be able to set up simple numerical simulations.
• Students will know how to perform data analysis on simulational data.
• Students will be able to apply mathematical tools to study statistical problems.

Teaching methods

• Laptop seminar
• Lecture
• Self-study
• homework assignments

The homework assignments provide students with an opportunity to conduct "computer experiments" and by such acquire much better intuition about the meaning of different classes of statistical behavior. The submission of  homework assignments  is a prerequisite for taking the final exam and constitute 20% of the final grade.

Learning activities

Attendance

Additional requirements for this course:

Students are strongly recommended to attend all lectures and exercise sessions.  The student may be absent in 2 out of  7 tutorial sessions.

Assessment

Assignments

There will be 2 homework assignments   that involve  numerical exercises. They will be  graded and their submission is prerequisite for taking the final exam.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Contact information

Coordinator

• dr. S. Jabbari Farouji

Teaching assistants: 

 Baptiste Parage (b.m.m.parage@uva.nl) 

Joy Sanghavi (j.k.sanghavi@uva.nl)

Vito Seinen  (v.t.seinen@uva.nl)