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## Module PH2015

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.

### Basic Information

PH2015 is a semester module in English language at Master’s level which is offered in winter semester.

This module description is valid to WS 2014/5.

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

150 h  h 5 CP

Responsible coordinator of the module PH2015 is the Dean of Studies at Physics Department.

### Content, Learning Outcome and Preconditions

#### Content

Topics:

• Non-equilibrium thermodynamics (entropy production, stationary non-equilibrium states, Onsager relations)
• Causality and Fluctuations (Kramers-Kronig relations, fluctuation-dissipation theorem)
• Stochastic Processes (Markov processes, Master equation approach, Brownian motion, Langevin equation, Fokker-Planck equation)
• Kinetic models (Boltzmann equation, H-Theorem, Enskog Method)

#### Learning Outcome

At the end of the module ASM-I students are able to formulate and classify simple non-equilibrium systems in terms of their entropy production and to derive response functions from the Fluctuation-dissipation theorem. They can derive the relation between different formalisms of describing stochastic processes. They have also insight into basic kinetic processes.

#### Preconditions

Keine Vorkenntnisse nötig, die über die Zulassungsvoraussetzungen zum Masterstudium hinausgehen.

### Courses, Learning and Teaching Methods and Literature

#### Learning and Teaching Methods

lecture, beamer presentation, board work, exercises in individual and group work

practise sheets

#### Literature

• Non-equilibrium thermodynamics, de Groot and Mazur
• The Fokker-Planck Equation, Risken
• Stochastic processes in physics and chemistry, N. G. van Kampen

### Module Exam

#### Description of exams and course work

In an oral exam the learning outcome is tested using comprehension questions and sample problems.

In accordance with §12 (8) APSO the exam can be done as a written test. In this case the time duration is 60 minutes.

#### Remarks on associated module exams

The exam for this module can be taken together with the exam to the associated follow-up module PH2016: Advanced Statistical Mechanics 2 / Fortgeschrittene Statistische Mechanik 2 after the follwoing semester. In this case you need to register for both exams in the following semester.

#### Exam Repetition

The exam may be repeated at the end of the semester. There is a possibility to take the exam in the following semester.

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