  Since the 1970s contact geometry has been recognized as an appropriate
framework for the geometric formulation of the state properties of
thermodynamic systems, without, however, addressing the formulation of
non-equilibrium thermodynamic processes. In Balian & Valentin (2001) it was
shown how the symplectization of contact manifolds provides a new vantage
point; enabling, among others, to switch between the energy and entropy
representations of a thermodynamic system. In the present paper this is
continued towards the global geometric definition of a degenerate Riemannian
metric on the homogeneous Lagrangian submanifold describing the state
properties, which is overarching the locally defined metrics of Weinhold and
Ruppeiner. Next, a geometric formulation is given of non-equilibrium
thermodynamic processes, in terms of Hamiltonian dynamics defined by
Hamiltonian functions that are homogeneous of degree one in the co-extensive
variables and zero on the homogeneous Lagrangian submanifold. The
correspondence between objects in contact geometry and their homogeneous
counterparts in symplectic geometry, as already largely present in the
literature, appears to be elegant and effective. This culminates in the
definition of port-thermodynamic systems, and the formulation of
interconnection ports. The resulting geometric framework is illustrated on a
number of simple examples, already indicating its potential for analysis and
control.
