28. Oktober 2026
Vortrag
Vortragender: Prof. Dr. Bernhard Maschke (Université Claude Bernard Lyon 1)
Vortragstitel: Open thermodynamic systems on homogeneous Lagrangian manifolds
Beginn: 16.15 Uhr
Ort: Seminarraum 2, Georg-Cantor-Haus
Abstract
In this talk, we shall present a control-theoretic formulation of the dynamics of open irreversible systems in the Thermodynamic Phase Space. In the first part, we shall briefly recall the geometric structure of the Thermodynamic Phase Space in terms of a contact manifold and the definition of the equilibrium properties of a system as a Legendre submanifold. We shall also recall how the Thermodynamic Phase Space may be lifted to a symplectic manifold where the equilibrium properties of a thermodynamic systems are defined as homogeneous Lagrangian submanifolds.
In the second part, we shall show how the reversible and irreversible transformations of thermodynamic systems may be expressed in terms of homogeneous Hamiltonian vector fields. We shall discuss the properties of the generating functions of these Hamiltonian vector fields and show how to construct them from the underlying state equations or systems of balance equations.
In the third part, we shall introduce input and output variables and consider homogeneous Hamiltonian control systems in order to represent open thermodynamic systems. And we shall present some preliminary results on the structure preserving feedback control of these systems.