Deriving a GENERIC system from a Hamiltonian system

Abstract: We reconsider the problem of coarse-graining infinite-dimensional Hamiltonian dynamics to obtain a macroscopic system that includes dissipative mechanisms. In particular, we study the thermodynamical implications concerning Hamiltonians, energy, and entropy and the induced geometric structures. The Hamiltonian model is described by a unitary group, and is time-reversible. The coarse-grained description includes dissipative effects, is described by a contraction semigroup, and is thus irreversible. The concepts of dilations and contractions will be described as they provide a link between dissipative semigroups and unitary groups. The coarse-grained version will be shown to have GENERIC (General Equations for Non-Equilibrium Reversible Irreversibe Coupling) structure, with conserved energy, nondecreasing entropy and an Onsager operator describing the dissipation.

This is joint work with Alex Mielke and Mark Peletier.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)