Arjan van der Schaft (University of Groningen)
Liouville geometry of thermodynamics
In the contact-geometric formulation of classical thermodynamics a distinction needs to be made between the energy and the entropy representation. By considering homogeneous coordinates for the intensive variables this distinction can be overcome. This results in a geometric formulation on the cotangent bundle of the manifold of extensive variables, where all geometric objects, in particular Lagrangian submanifolds and Hamiltonian vector fields, are homogeneous in the cotangent variables. The resulting geometry is a special type of symplectic geometry, called Liouville geometry. Additional homogeneity with respect to the extensive variables, corresponding to the classical Gibbs-Duhem relation, can be treated within the same framework. The theory will be illustrated on a number of simple physical examples.