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327-5103-00L 4 Credits MSC D-MATL , D-PHYS , D-MATH

Nonequilibrium Statistical Mechanics

Lecturers & Examiners: Prof. em. Dr. Hans Christian Öttinger
VVZ CR n/a

Last Updated: 2026-02-05 15:29:36

Abstract

Foundations of nonequilbrium statistical mechanics based on a unified approach, including projection-operator method, linear response theory, fluctuation-dissipation theorem, kinetic theory of gases, Boltzmann's equation, Chapman-Enskog Method, Grad's Moment Expansion, kinetic theory of polymeric liquids, simulation techniques (Monte Carlo, Brownian dynamics, molecular dynamics)

Objective

To provide, illustrate, and practice the thermodynamic recipes for bridging length and time scales in nonequilibrium systems, including an overview of the roles of various simulation techniques

Content

1. Projection-Operator Method: Notation of Classical Mechanics, Ensembles, Projection Operators, Atomistic Expressions, Exact Time-Evolution Equation, Markovian Approximation, Linear Response Theory, Probability Density Approach, Fluctuation-Dissipation Theorem, Relationship Between Coarse-Grained Levels, Quantum Systems 2. Kinetic Theory of Gases: Elementary Kinetic Theory, Mean Free Path, Transport Coefficients, Boltzmann's Equation, Differential Cross Section for Collisions, Projection-Operator Approach, Chapman-Enskog Method, Grad's Moment Expansion, Thirteen-Moment Expansion, Structured Moment Method 3. Simulations: Simulation Philosophy, Understanding Through Simplicity, Overview over Simulation Techniques, Monte Carlo Simulations, Markov Chains, Detailed Balance, Brownian Dynamics, Stochastic Differential Equations, Dilute Polymer Solutions, Molecular Dynamics, Expressions for the Friction Matrix, Verlet-Type Integrators, Rarefied Len¬nard-Jones Gas, Entangled Polymer Melts

Resources

Lecture Notes

The course is based on the book "Beyond Equilibrium Thermodynamics"

Literature

1. H. C. Öttinger, Beyond Equilibrium Thermodynamics (Wiley, New York, 2005) 2. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer-Verlag, Berlin 1985)

General Information

Language
English
Levels
MSC
Frequency
Yearly recurring

Examination

Type
end-of-semester examination

Course Components

Type Title Time & Place Hours
lecture Nonequilibrium Statistical Mechanics
Bitte rechtzeitig den Dozenten kontaktieren. Please contact the lecturer in good time.
  • By Appointment None-None
2 h weekly
exercise Nonequilibrium Statistical Mechanics
Bitte rechtzeitig den Dozenten kontaktieren. Please contact the lecturer in good time.
  • By Appointment None-None
2 h weekly

Offered In