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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
TIF150 - Information theory for complex systems
Syllabus adopted 2014-02-13 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
The course is open for exchange students
Block schedule: B

Course elements   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0107 Examination 7,5c Grading: TH   7,5c   20 Mar 2015 pm M,  Given by dept,  20 Aug 2015 am V

In programs



Professor  Kristian Lindgren

Course evaluation:

Homepage missing



In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

Basic undergraduate mathematics and probability theory.


The course introduces the students to important concepts in information theory that can be used to describe and characterise complex systems. The concepts are applied to a number of areas in complex systems: cellular automata, fractals, chemical self-organisation, and chaos. The main aim is to give students the knowledge and skills to apply information theory to a wide variety of different systems. The course also gives a presentation of the connections between information theory and physics, primarily statistical mechanics and thermodynamics.

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

After successfully completing this course the students will be able to

Define and use the basic concepts of information theory: Shannon entropy, relative entropy, complexity measures based on these
Use information theory to characterise both cellular automata and low-dimensional chaos
Understand the connection between information theory and statistical mechanics
Use geometric information theory to characterise patterns in spatically extended systems like pictures
Explain how information is flowing in chemical self-organising systems exhibiting pattern formation


Basic concepts of information theory
- Shannon entropy, relative information, complexity measures
Information theory for symbol sequences and lattice systems
- correlations and randomness in symbol sequences
Information theory and physics
- entropy in physics and its relation to randomness in information theory
Cellular automata
- order and disorder in the time evolution of various cellular automaton rules
Geometric information theory
- presentation of an information-theoretic framework for characterising patterns
Self-organising chemical systems
- flows of information in the process of pattern formation
Chaotic systems and information
- flows of information from micro to macro in chaotic systems


The course is based on a series of lectures, in total 30 hours, covering the topics listed above. Every week a set of home assignments are distributed. An optional mini project can also be done.


K. Lindgren,  Information theory for complex systems - An information perspective on complexity in dynamical systems, physics, and chemistry. Lecture notes, Chalmers, 2014.


The examination will be based on a final written exam, with possibility of extra points from homework assignments and the optional mini project.

Published: Fri 18 Dec 2009. Modified: Mon 28 Nov 2016