Course syllabus for Non-equilibrium processes in physics, chemistry and biology

Course syllabus adopted 2026-02-19 by Head of Programme (or corresponding).

Overview

  • Swedish nameIcke-jämviktsprocesser i fysik, kemi och biologi
  • CodeTIF106
  • Credits7.5 Credits
  • OwnerMPCAS
  • Education cycleSecond-cycle
  • Main field of studyBioengineering, Chemical Engineering, Engineering Physics
  • DepartmentPHYSICS AND ASTRONOMY
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language

    English

  • Application code

    11120

  • Block schedule

  • Open for exchange students

    Yes

Credit distribution

Module
Sp1
Sp2
Sp3
Sp4
Summer
Not Sp
Examination dates
0111 Examination 7.5 c
Grading: TH		 7.5 c

In programmes

Examiner

Eligibility

General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements

Course specific prerequisites

Analysis and Linear Algebra. Knowledge of the basics of statistical physics is an advantage but not required.

Aim

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.

Learning outcomes (after completion of the course the student should be able to)

  • explain basic concepts of probability theory and stochastic processes
  • explain central stochastic processes in physics, chemistry, and biology
  • formulate diffusion models for stochastic physical, chemical, and biological systems
  • solve Langevin and Fokker-Planck equations using standard analytical methods and numerical simulations

Content

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

Organisation

Lectures and exercises.

Literature

  • Lennart Sjögren, lecture notes "Stochastic processes", available as PDF
  • N.G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland (2007)
  • P. L. Krapivsky, S. Redner & E. Ben-Naim, A kinetic view of statistical physics, Cambridge University Press (2010)
  • P.M. Chaikin & T.C. Lubensky, Principles of condensed matter physics, Cambridge University Press (1995), Chapter 8

Examination including compulsory elements

Written examination. There are optional exercise problems that give bonus points that can contribute to the grade.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers about disability study support.