Geometry of Thermodynamic Processes
AbstractSince the 1970s, contact geometry has been recognized as an appropriate framework for the geometric formulation of thermodynamic systems, and in particular their state properties. More recently it has been shown how the symplectization of contact manifolds provides a new vantage point; enabling, among other things, to switch easily 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, is extended to 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. View Full-Text
Share & Cite This Article
van der Schaft, A.; Maschke, B. Geometry of Thermodynamic Processes. Entropy 2018, 20, 925.
van der Schaft A, Maschke B. Geometry of Thermodynamic Processes. Entropy. 2018; 20(12):925.Chicago/Turabian Style
van der Schaft, Arjan; Maschke, Bernhard. 2018. "Geometry of Thermodynamic Processes." Entropy 20, no. 12: 925.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.