Nonequilibrium Statistical Mechanics

Lecturer(s)

Prof. H.C. Öttinger

Hour(s) of lecture(s), exercise(s) and credit points

2L
2E
4CP

Teaching goals

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

Summary and outline

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

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

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 Lennard-Jones Gas, Entangled Polymer Melts

Literature

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

The course is based on Part 2 of the book Beyond Equilibrium Thermodynamics »».
Familarity with Part 1 »» is required.