260089 VO Deterministisches Chaos II (2006S)

ECTS Points: 3
This is the second part of a two-semester course on deterministic chaos and its application to statistical physics and, in particular, to processes far from thermodynamic equilibrium. Nonlinear-system theory provides an explanation
for the Second Law of thermodynamics and for the irreversibility of macroscopic processes in spite of the time reversibility of the underlying equations of motion. It allows to derive new relations connecting the stability of the phase-space trajectory with the properties of the transport processes involved. Chaos in Hamiltonian systems is also treated, where the examples range from the simple pendulum to the stability of the solar system.

The topics include: Renyi dimensions of fractal attractors; singularity spectrum of multifractals and the thermodynamic formalism; Lyapunov instability; mechanics revisited: nonholonomic constraints and computer thermostats; Gauss and Nose-Hoover mechanics; systems far from thermodynamic equilibrium; transport theory; generalized Liouville equation; linear response theory; nonequilibrium molecular dynamics (NEMD) and nonequilibrium stationary states (NESS), pressure tensor and virial theorem; conductivity, viscosity, and diffusion; microphysics - macrophysics and the Second Law; resolution of Loschmidt's paradox; attractors and repellors for ergodic and stationary nonequilibrium flows; Hamiltonian flows; Poincare integral invariants; KAM theorem; the
rings of Saturn; stability of the solar system.

The course is complemented by computer exercises designed to illuminate various topics.