Dirac Structures in Open Thermodynamics

Abstract

Dirac structures are geometric objects that generalize Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems and play an essential role in the understanding of the interrelations between system elements in implicit dynamical systems. In this paper, we show how nonequilibrium thermodynamic systems can be naturally understood in the context of Dirac structures, by mainly focusing on the case of open systems, i.e., thermodynamic systems exchanging heat and matter with the exterior.