  In the contact-geometric formulation of classical thermodynamics distinction
is made between the energy and entropy representation, which can be resolved by
taking homogeneous coordinates for the intensive variables. This results in a
geometric formulation on the cotangent bundle of the manifold of extensive
variables, where all geometric objects are homogeneous in the cotangent
variables. The resulting geometry is studied in-depth. Additional homogeneity
with respect to the extensive variables, corresponding to the classical
Gibbs-Duhem relation, is treated within the same geometric framework.
