Universität Wien

260008 VO Advanced Statistical Physics and Soft Matter Physics (2023W)

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

An/Abmeldung

Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").
Für diese LV an-/abmelden

Details

Sprache: Englisch

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

  • Dienstag 03.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Freitag 06.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Dienstag 10.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Freitag 13.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Dienstag 17.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Freitag 20.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Dienstag 24.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Freitag 27.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Dienstag 31.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Freitag 03.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Dienstag 07.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Freitag 10.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Dienstag 14.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Freitag 17.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Dienstag 21.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Freitag 24.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Dienstag 28.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Freitag 01.12. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Dienstag 05.12. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Dienstag 12.12. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Freitag 15.12. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Dienstag 09.01. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Freitag 12.01. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Dienstag 16.01. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Freitag 19.01. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
  • Dienstag 23.01. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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

Tentative table of contents:

1. Equilibrium thermodynamics and statistical mechanics in a nutshell

1.1. Thermodynamics (first and second law, equiibrium conditions)
1.2. Statistical mechanics (ensembles, fluctuations)

2. Non-equilibrium thermodynamics

2.1. Balance equations (entropy production)
2.2. Phenomenological equations and Onsager relations

3. Non-equilibrium statistical mechanics

3.1. Fluctuations and microscopic reversibility
3.2. Microscopic derivation of Onsager relations
3.3. Linear Response theory and transport phenomena (fluctuation-dissipation theorem)
3.4. Brownian motion and Langevin equations
3.5. Fokker-Planck equations
3.6. Master equations
3.7. Stochastic thermodynamics (Jarzynski and Crooks theorems)
3.8. Kinetic theory (Boltzmann equation)

Art der Leistungskontrolle und erlaubte Hilfsmittel

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.

Mindestanforderungen und Beurteilungsmaßstab

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

Prüfungsstoff

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.

Literatur

The following books are useful:

S.R. de Groot, P. Mazur, Non-equilibrium thermodynamics, Dover Publications, 1984
E.M.Lifshitz, L.P.Pitaevskii, Physical Kinetics, Butterworth-Heinennan, 1981
N.G. van Kampen, Stochastic processes in physics and chemistry, Elsevier, 2007
C. Gardiner, Stochastic methods, Springer, 2009
D. J. Evans, G. Morriss, Statistical Mechanics of Nonequilibrium Liquids, AIP Press, 1994
J. P. Boon, S. Yip, Molecular Hydrodynamics, McGraw-Hill, 1980.
R. Livi, P. Politi, Nonequilibrium Statistical Physics, A Modern Perspective, Cambridge University Press, 2017
R. Zwanzig, Non-equilibrium Statistical Mechanics, Oxford University Press, 2001
R. Kubo, M. Toda, N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics, Springer Verlag, 1991
L. Peliti and S. Pigolotti, Stochastic Thermodynamics, Princeton University Press, 2023
K. Huang, Statistical Mechanics, John Wiley, 1987

Zuordnung im Vorlesungsverzeichnis

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

Letzte Änderung: Do 28.09.2023 11:48