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Non-Equilibrium Statistical Physics

Module PH2229

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of SS 2018 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2018WS 2015/6

Basic Information

PH2229 is a semester module in English language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for condensed matter physics
  • Complementary catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for Biophysics
  • Complementary catalogue of special courses for Applied and Engineering Physics
  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
300 h 90 h 10 CP

Responsible coordinator of the module PH2229 is Wilhelm Zwerger.

Content, Learning Outcome and Preconditions


I) Non-Equilibrium Dynamics of Classical Systems

1) Onsager Theory, Minimal Entropy Production
2) Boltzmann Equation, H-Theorem
3) Navier-Stokes Equation, Hydrodynamic Modes
4) Long-Time Tails, Fluctuating Hydrodynamics in 1D, KPZ-Equation  5) Turbulence, Kolmogorov Spectrum
6) Dynamical Scaling near Continuous Phase Transitions

II) Non-Equilibrium Dynamics of Quantum Systems

1) Linear Response, Relaxation and Ergodicity Breaking  2) Kibble-Zurek Dynamics
3) Lieb-Robinson bounds
4) Periodically Driven (Floquet) Systems
5) Anderson versus Many-Body Localization

Learning Outcome

The students will learn the basic methods of Non-Equlibrium Thermodynamics and Statistical Physics together with their applications in a wide range of problems, with an emphasis on examples from Condensed Matter and Many-Body Physics. Both classic topics (Boltzmann-Equation, Linear Response, Scaling and Turbulence) as well as topics of current interest are covered (Lieb-Robinson bounds, Floquet systems, Many-Body Localization). The course will thus prepare students for independent research projects.


The course is a continuation of the Lecture on Thermodynamics and Statistical Physics of the previous semester, which is a necessary requirement. In addition, a good knowledge of Quantum Mechanics and standard mathematical methods like Fourier-Transformation is assumed.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 4 Non-Equilibrium Statistical Physics Zwerger, W. Tue, 10:00–12:00, PH 3343
Thu, 10:00–12:00, PH 3343
UE 2 Exercise to Non-Equilibrium Statistical Physics
Responsible/Coordination: Zwerger, W.
Wed, 16:00–18:00, PH-Cont. C.3203

Learning and Teaching Methods

In the thematically structured lecture the learning content is presented. A proper understanding of the contents of the lecture will be verified through the weekly exercise classes. In particular, students are required to present the solution of the elementary parts of the exercise problems on the blackboard.


no info


  • R. Balian: From Microphysics to Macrophysics, Volume 2
  • D. Forster: Hydrodynamic Fluctuations, Broken Symmetry and Correlation Functions
  • Specific literature will be given for chapters I.4-6 and II.2-5

Module Exam

Description of exams and course work

There will be an oral exam of 30 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

  • Write down the basic evolution equations in non-equilibrium thermodynamics (Onsager, Boltzmann)
  • Sketch methods of their solution (relaxation time approximation, ...)
  • Write down the definitions of linear response and correlation functions and their interrelations (Fluctuation-Dissipation Theorem, Kramers-Kronig relations)
  • Write down scaling solutions for transport coefficients or for spectra far from equilibrium (Kolmogorov)
  • Formulate the basic theorems for Floquet systems in terms of the quasi-energy spectrum

Exam Repetition

The exam may be repeated at the end of the semester.

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