Arjan van der Schaft (RuG)
Geometric modeling and control of thermodynamic systems
Starting from Gibbs fundamental relation, contact geometry has been recognized as an appropriate framework for the geometric modeling of thermodynamic systems. Recently, the interest in contact-geometric descriptions of thermodynamics has been intensified. In particular, this has led to the theory of contact control systems. On the other hand, it is well-known in geometry (see e.g. Appendix 4 in Arnold’s book on classical mechanics) that contact manifolds can be naturally symplectified to symplectic manifolds with an additional structure of homogeneity. However, the applications of, and motivations for, this theory seem to have been confined to time-dependent Hamiltonian mechanics, or partial differential equations. Only in a paper by Balian and Valentin it was argued that the symplectification of contact manifolds provides a new and insightful view point to thermodynamics as well. In this paper, motivated by control problems in multi-physics systems (including thermodynamic components), we will further expand the symplectification point of view.