Nonequilibrium Physics with Interdisciplinary Applications

### Time and Location:

Time: Tuesday, 10:00 - 11:30 Uhr (tutorial: 11:30 - 12:00)

Place: Seminar room Institute for Theoretical Physics

### Topic:

The course will introduce the basic concepts and methods of
nonequilibrium physics and stochastic systems. These will be
illustrated using examples from interdisciplinary applications.
Examples are:
- Stochastic processes and their description (Master-,
Fokker-Planck equation)
- Basic models (random walk, cellular automata models)
- Analytical and numerical methods
- Phase transitions
- Traffic (jam formation, phases, models)
- Pedestrian dynamics (collective effects, evacuations)
- Biological systems (ant trails, intracellular transport)
- Socio-economic systems (stock market, auctions, supply chains)
- Game theory (chip distribution in Poker, Ebay auctions)
- Pattern formation

### Audience, requirements:

The course is part of the master course, e.g. as specialised course
(4 credit points) in "Statistical and Biologicial Physics"

Knowledge in statistical physics is helpful, but not essential.

### Exercises:

Problem sheet 1

Problem sheet 2

Problem sheet 3

Problem sheet 4

Problem sheet 5

Problem sheet 6

Problem sheet 7

Problem sheet 8

Problem sheet 9

Problem sheet 10

### Materials:

Simulation of
the Nagel-Schreckenberg model

Universal statistical properties of poker tournaments

Poker
(slides)

Flashing ratchet
(Java applet)

Ratchets (slides)

Brownian motion (Java applet)

### Literature:

- A. Schadschneider, D. Chowdhury, K. Nishinari:
*Stochastic Transport in Complex Systems* (Elsevier, 2010)
- P.L. Krapivsky, S. Redner, E. Ben-Naim:
*A Kinetic View of Statistical
Physics* (Cambridge University Press, 2010)
- V. Privman (Ed.):
*Nonequilibrium Statistical Mechanics in One
Dimension* (Cambridge University Press, 1997)
- N.G. van Kampen:
*Stochastic Processes in Physics and Chemistry*
(North Holland)
- B. Chopard, M. Droz:
*Cellular Automaton Modeling of Physical Systems*
(Cambridge University Press)
- R. Mahnke, J. Kaupuzs, I. Lubashevsky:
*Physics of Stochastic Processes: How Randomness Acts in Time*
(Wiley VCH, 2008)
- N. Boccara:
*Modeling Complex Systems* (Springer)
- G.M. Schütz:
*Exactly solvable models for many-body systems
far from equilibrium*, in Phase Transitions and Critical Phenomena,
Vol.19, hrsg. von C. Domb and J.L. Lebowitz (Academic Press)
- D. Chowdhury, K. Nishinari, A. Schadschneider:
*Physics of transport
and traffic phenomena in biology: from molecular motors and cells
to organisms*, Physics of Life Reviews 2, 318 (2005)
PDF
- D. Chowdhury, K. Nishinari, A. Schadschneider:
*Self-organized patterns and traffic flow in colonies of organisms:
from bacteria and social insects to vertebrates*,
Phase Trans. 77, 601 (2004)
PDF
- D. Chowdhury, L. Santen, A. Schadschneider:
*Statistical Physics of Vehicular Traffic and Some Related Systems*,
Physics Reports 329, 199 (2000),
PDF

- D. Helbing:
*Traffic and related self-driven many-particle systems*,
Rev. Mod. Phys. 73, 1067 (2001),
PDF