Universität Wien
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260008 VO Advanced Statistical Physics and Soft Matter Physics (2024W)

6.00 ECTS (4.00 SWS), SPL 26 - Physik
Moodle

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Details

Language: English

Lecturers

Classes (iCal) - next class is marked with N

Achtung: Erste Vorlesung am Freitag 4.10., 9.00-10:30

  • Tuesday 01.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Friday 04.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Tuesday 08.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Friday 11.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Tuesday 15.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Friday 18.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Tuesday 22.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Friday 25.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Tuesday 29.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Tuesday 05.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Friday 08.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Tuesday 12.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Friday 15.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Tuesday 19.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Friday 22.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Tuesday 26.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Friday 29.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Tuesday 03.12. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Friday 06.12. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Tuesday 10.12. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Friday 13.12. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Tuesday 17.12. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Tuesday 07.01. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Friday 10.01. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Tuesday 14.01. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Friday 17.01. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Tuesday 21.01. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Friday 24.01. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien

Information

Aims, contents and method of the course

Non-equilibrium thermodynamics and statistical mechanics

Statistical mechanics has been very successful at describing physical systems at equilibrium. However, in nature and technology many phenomena occur under non-equilibrium conditions and their theoretical treatment is challenging. This course will give an introduction to the theoretical concepts and mathematical tools needed to describe time-dependent irreversible phenomena in systems away from equilibrium. The course will start with a quick reminder of the basic notions of equilibrium thermodynamics and statistical mechanics, although it is assumed that the participants have already taken a class on these topics at the level of T4. We will then introduce the fundamentals of phenomenological irreversible thermodynamics and discuss the macroscopic equations governing the transport of mass, momentum and energy. The main part of the course deals with statistical-mechanical treatment of time-dependent processes on the microscopic and mesoscopic scale. We will learn how linear response theory can be used to understand the behavior of systems close to equilibrium in terms is their equilibrium fluctuations. In subsequent chapters of the course, we will learn about how to describe non-equilibrium phenomena as stochastic processes, both in terms of stochastic differential equations (Langevin equation) and stochastic partial differential equations (Fokker-Planck equation). Recent exact results obtained for systems driven arbitrarily far from equilibrium, such as the Jarzynski equality and the Crooks fluctuation theorem, will be discussed in the chapter on stochastic thermodynamics. Finally, we will examine the basic ideas and results of kinetic theory including the Boltzmann equation and the H-theorem following from it.

The lectures will be complemented by weekly exercise sessions, in which the concepts discussed in class will be applied to solve specific problems either analytically or computationally.

After taking this course, students
- have an overview of the basic ideas and methods of non-equilibrium thermodynamics and statistical mechanics
- understand their range of applicability and know their limitations
- are able to apply the concepts and tools discussed in the course to solve concrete problems
- are prepared to read the current research literature in this field

Table of contents:

1. Equilibrium thermodynamics and statistical mechanics in a nutshell

1.1 Thermodynamics
1.2 Statistical mechanics

2. Non-equilibrium thermodynamics

2.1 Conservation laws
2.2 Entropy balance
2.3 The phenomenological equations

3 Non-equilibrium statistical mechanics - Linear Response Theory

3.1 Systems close to equililbrium
3.2 Non-equilibrium averages
3.3 Onsager's regression hypothesis and time correlation functions
3.4 Diffusion
3.5 Fluctuation-dissipation theorem
3.6 Response functions

4 Stochastic Processes

4.1 Brownian motion and the Langevin equation
4.2 Correlation functions and Brownian motion
4.3 Langevin equation in several variables
4.4 Non-Markovian Langevin equation
4.5 Fokker-Planck equation

5 Stochastic thermodynamics

5.1 Energy, work and heat
5.2 Crooks fluctuation theorem
5.3 Jarzynski equation

Assessment and permitted materials

There will be a written final exam in which students will have to answer questions about the content of the course and solve some problems at the level of the problems treated in the exercise class.

Minimum requirements and assessment criteria

For a positive grade it is necessary to achieve 50% of the total possible points at the final exam.

Examination topics

All topics discussed in class and in the exercise sessions will be relevant for the exam. For mastering the subjects of this course, the individual work on the weekly problem sets is very important.

Reading list

Association in the course directory

M-CORE 6, M-VAF A 1, UF MA PHYS 01a, UF MA PHYS 01b

Last modified: Fr 27.09.2024 17:26