# NON-EQUILIBRIUM PHYSICS WS 18/19

Lectures: Mon,Wed 12:00-14:00 D6-135

Tutorials: Fri 14:00-16:00 U2-232

Instructor: Jun.-Prof. Dr. Soeren Schlichting

(sschlichting AT physik.uni-bielefeld.de)

Tutor: Dennis Schroeder

(dennis AT physik.uni-bielefeld.de)

This graduate (M.Sc.) level course provides an introduction to non-equilibrium statistical physics, based on the book of * N. Pottier * on *``Nonequilibrium Statistical Physics``*

Topics include:

- Thermodynamics of irreversible processes- Statistical description of non-eq. systems

- Kinetic theory

- Weak wave turbulence

- Stochastic processes

- Linear repsonse theory

Course materials and exercise sheets will become available below over the course of the semester.

Course evaluation for Lectures and Tutorials .

Exercise sheets:

Course materials:

Week 1 -- Thermodynamics of irreversible processes: Equilibrium thermodynamics (reminder), Description of irreversible processes, Local equilibrium, Entropy production in discrete & continuous systems

Notes from Oct 8th and Notes from Oct 10th

Week 2 -- Thermodynamics of irreversible processes: Linear irreversible proccesses, Simple transport phenomena, Curie and Onsager relations

Notes from Oct 15th

Week 3 -- Thermodynamics of irreversible processes: Coupled transport phenomena, Dynamics of simple fluids, Navier-Stokes equation

Notes from Oct 22th and Notes from Oct 24th

Week 4 -- Thermodynamics of irreversible processes: Simple problems in fluid dynamics

-- Statistical description of non-equilibrium systems: Description of classical & quantum systems

Notes from Oct 22th and Notes from Oct 24th

Week 5 -- Statistical description of non-equilibrium systems: Wigner-Weyl formalism

Notes from Nov 5th and Nov 7th

Week 6 -- Statistical description of non-equilibrium systems: Non-equilibrium path integral, reduced phase-space distributions

Notes from Nov 12th and Notes from Nov 14th

Week 7 -- Statistical description of non-equilibrium systems: BBGKY Hierarchy, Boltzmann equation

Notes from Nov 19th and Notes from Nov 21st

Week 8 -- Kinetic theory/Boltzmann equation: Balance equations, Statistical entropy, H-Theorem

Notes from Nov 26th and Notes from Nov 28th

Week 9 -- Kinetic theory/Boltzmann equation: Equilibrium solutions, Hilbert expansion, Relaxation Time Approximation

Notes from Dec 3rd and Notes from Dec 5th

Week 10 -- Kinetic theory/Boltzmann equation: Calculation of transport coefficients, Hydrodynamic limit

Notes from Dec 10th and Notes from Dec 12th

Week 11 -- Kinetic theory/Boltzmann equation: Hydrodynamic limit

Notes from Dec 17th

-- Wave turbulence: Stationary turbulence, Richardson cascade, Kolmogorov-Zhakarov spectra
Notes from Dec 19th

See also textbook V.E. Zakharov, V.S. L'vov and G. Falkovich; Kolmogorov Spectra of Turbulence I: Wave turbulence (Chapters 1,2,3)

Week 12 -- Stationary turbulence: Kolmogorov-Zhakarov spectra, Energy cascade, Decaying turbulence

Notes from Jan 7th and Notes from Jan 9th

See also textbook S. Nazarenko; Wave turbulence (Chapter 9)

Week 13 -- Stochastic processes: Brownian motion, Fluctuation Dissipation relations

Notes from Jan14th and Jan 16th

Week 14 -- Stochastic processes: Kramers-Moyal expansion, Fokker-Planck equations

Notes from Jan 21st and Notes from Jan 23rd

Week 15 -- Linear response theory: Derivation of Kubo formula, Fluctuation Dissipation relations

Notes from Jan 28th and Jan30th