Article Geometry of Thermodynamic Processes Arjan van der Schaft 1, and Bernhard Maschke 2 1 Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, Jan C. Willems Center for Systems and Control, University of Groningen, the Netherlands;
[email protected] 2 Univ. Lyon 1, Université Claude Bernard Lyon 1, CNRS, LAGEP UMR 5007, Villeurbanne, France;
[email protected] * Correspondence:
[email protected]; Tel.: +31-50-3633731 Received: date; Accepted: date; Published: date Abstract: 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 [3] 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 [2,18], appears to be elegant and effective. This culminates in the definition of port-thermodynamic systems, and the formulation of interconnection ports.