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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
TIF106 - Non-equilibrium processes in physics, chemistry and biology
Syllabus adopted 2012-02-22 by Head of Programme (or corresponding)
Owner: MPCAS
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: Second-cycle
Major subject: Bioengineering, Chemical Engineering, Engineering Physics
Department: 16 - PHYSICS

Teaching language: English
Open for exchange students
Block schedule: D

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0111 Examination 7,5c Grading: TH   7,5c   28 May 2013 pm V,  26 Aug 2013 am M

In programs



Univ lektor  Lennart Sjögren
Professor  Vitaly Shumeiko


MCC010   Statistical physics II TIF105   Stochastic processes in physics, chemistry and biology

Course evaluation:

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For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

Mathematical analysis and Algebra. Introductory level Thermodynamics and Statistical Physics, Classical and Quantum Mechanics


The great majority of physical, chemical, and biological processes occur
outside the thermodynamic equilibrium. How do we describe many-particle
system driven away from equilibrium, or evolving towards the equilibrium
due to an interaction with an environment? In contrast to the universality
of the thermodynamics, the non-equilibrium evolution is system specific
and requires individual approach. The purpose of the course is to
introduce basic concepts of kinetic theory and stochastic processes,
and to study practical tools to investigate non-equilibrium states. We will discuss the origin
of irreversible evolution and dissipation, hierarchy of relaxation processes, transport phenomena and noise, Brownian motion.
The course includes a selection of applications to quantum solid state systems,
chemical reaction kinetics, and soft matter like colloidal dispersions, polymers, gels,
glasses and biological systems.

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

In this course the student should acquire a general knowledge of stochastic processes and their use to describe the time evolution of systems in nature; the student will learn basic concepts and practical methods of the kinetic theory for classical and quantum many body systems. The following topics are covered: Statistical description of a dissipative macroscopic system and origin of irreversible evolution. Stochastic processes and basic distributions. Boltzmann equation and transport theory. Langevin theory of classical and quantum Brownian motion. Fluctuation and noise. Applications to physical, chemical and biological systems.

After having taken "Non-equilibrium processes in physics, chemistry and biology"
the student should have acquired

* knowledge of basic concepts and practical methods of the kinetic theory for classical and quantum many particle systems
* understanding the origin of irreversible evolution of physical, chemical, and biological systems, and hierarchy of relaxation processes
* practical skills in solving transport problems, analyzing dissipative and fluctuation phenomena, and effects of environment.
* a general knowledge of stochastic processes and their use to describe the time evolution of systems in nature.


The first half of the course deals with general concepts of non-equilibrium statistical physics and methods to describe dissipative and transport processes in many-body systems. Starting with a simple example of a random walk the basic concepts in probability theory and stochastic processes are introduced. More complex systems are studied via the Boltzmann equation and by considering Markov processes. The latter introduces the study of Master-, Fokker-Planck- and Langevin equations.

The student can choose two different directions for the second part of the course:

1. Quantum non-equilibrium systems
Here we consider applications in modern solid state physics, quantum electronics and optics. We study methods to describe the state and evolution of quantum non-equilibrium systems, linear response theory, problem of quantum noise, relation between fluctuations and dissipation, behavior of quantum particle in an environment.

2. Transport in soft matter and biological systems
Here we study applications in complex systems. We study methods to describe transport processes in various systems like polymers, colloids, soft matter. Description of chemical reactions and Brownian motors. Applications to systems in phsyics, chemistry and biology.


The course is based on a series of lectures and exercises. The second half of the course can be organized as a project work.


The content of the course will be covered in lecture notes. Additional reading material (course book) will be specified on the course homepage.


Home assignmnets and written examination

Page manager Published: Thu 04 Feb 2021.