Syllabus
Principle of least action and Hamilton's canonical equations. Basics of differential geometry, Lie groups, Lie algebras, dual of a Lie algebra, Euler-Poincaré equations of motion. Rotation of a rigid body. Semidirect product and a heavy spinning top. Infinite-dimensional Lie groups and fluid mechanics. Continuum mechanics i Lagrangian and Eulerian description, solid matter, viscoelastical fluids and fluid mechanics.
(Ir)reversibility with respect to time inversion. Dissipation potential, entropic and energetic representation. Entropy growth. General Equation for Non-equilibrium Reversible-Irreversible Coupling (GENERIC). Maximum entropy principle (MaxEnt).
Liouville equation and kinetic theory. Electromagnetic field and its interaction with matter. Mixtures. Maxwell-Stefan equations, Fick and Ohm Laws. Hyperbolic heat transfer and Fourier Law.
Annotation
The goal (probably unattainable) of non-equilibrium thermodynamics is to describe systematically all natural processes on different levels of description. The aim of the course is to introduce General Equation for Non- equilibrium Reversible-Irreversible Coupling (GENERIC), a theory combining Hamiltonian mechanics with gradient dynamics, connecting complex mechanical behaviour with thermodynamical evolution.
GENERIC seems to be a promising path to the goal of non-equilibrium thermodynamics.