NFYK24002U Physics of Nonequilibrium Systems

Volume 2024/2025

MSc Programme in Physics


Most phenomena in nature take place under non-equilibrium conditions which, for instance, can be associated to temperature, electrical field, or concentration gradients. They are driven by thermodynamic forces and fluxes, and they dissipate energy and produce entropy. Many processes in biology can serve as examples, but also open systems that deal with climate and tipping points. Further examples are thermal osmosis, the thermoelectric effect, and oscillating chemical reactions. Nonequilibrium theory also determines relaxation behavior and fluctuation lifetimes, i.e., the timescales of physical processes. Even reversible oscillatory processes like an oscillating spring or belong to systems that can be described by nonequilibrium theory.

This course introduces into the thermodynamics of irreversible processes and into the application of these concepts to elementary biological reactions and to systems of general physical importance. We derive Onsager's phenomenological equations and the reciprocal relations. We derive important fluctuation theorems, e.g., the Jarzynski equality. As an important example, this course also introduces into the physics of nerve pulses. We contrast classical dissipative theory of nerves with an adiabatic hydrodynamic treatment of nerves leading to the possibility of solitons in membranes. Both are examples for nonequilibrium processes.

Learning Outcome

Thermodynamic forces and fluxes as well as theory of fluctuations and theory of nerves.


Understanding of thermodynamics from the point of view of an entropy potential, and the important examples in the theory of nerves pulse transmission.


After this course students should be able to:

  • Derive the Hodgkin-Huxley model
  • Describe the hydrodynamics of the nerve pulse
  • Handle the entropy as a potential
  • Derive cycle kinetics and its application to ion pumps
  • Work with thermodynamic forces and fluxes
  • Work with Onsager's equations, and understand the concept of microscopic reversibility

See Absalon for final course material. The following is an example of expected course litterature.


There will be handouts that are sufficient to understand the course.

Recommended is the reading of: "Modern Thermodynamics: From Heat Engines to Dissipative Structures (Paperback) by D. Kondepudi and I. Prigogine".

Physics bachelor, Chemists and Biologists with previous training in
Previous knowledge in thermodynamics is
of advantage.

Academic qualifications equivalent to a BSc degree is recommended.
Lectures and exercises
  • Category
  • Hours
  • Lectures
  • 42
  • Preparation
  • 146,5
  • Theory exercises
  • 14
  • Guidance
  • 3
  • Exam
  • 0,5
  • Total
  • 206,0

Students have to give oral presentations about historical papers during the course, which are discussed with the class.

7,5 ECTS
Type of assessment
Oral examination, 30 minutes (no preparation time)
Type of assessment details
The course will be split in 6 major topics. The candidate gives a free 15 minute presentation of one of these subjects. The topic is chosen by rolling a die.
During the remaining 15 minutes of the exam questions about the other five topics will be asked by the course leader or the censor.
Exam registration requirements

During the exercises student will present short oral contributions about historical papers. The oral presentation is mandatory.

Only certain aids allowed

Lecture notes are not allowed during the exam. One card with key words is allowed for each topic (six in total).

The cards shall help the student to recall the prepared structure of the presentations, but shall not contain detailed derivations.

Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners

Same as ordinary exam.

If the exam prerequisite has not been fulfilled, the student must contact the course responsible well in advance in order to arrange to give a presentation no later than 2 weeks before the re-exam.

Criteria for exam assesment

See Learning outcome