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In this paper, we introduce the notion of port-Lagrangian systems in nonequilibrium thermodynamics, which is constructed by generalizing the notion of port-Lagrangian systems for nonholonomic mechanics proposed in Yoshimura and Marsden [2006c], where the notion of interconnections is described in terms of Dirac structures. The notion of port-Lagrangian systems in nonequilibrium thermodynamics is deduced from the variational formulation of nonequilibrium thermodynamics developed in Gay-Balmaz and Yoshimura [2017a,2017b]. It is a type of Lagrange-dAlembert principle associated to a specific class of nonlinear nonholonomic constraints, called phenomenological constraints, which are associated to the entropy production equation of the system. To these phenomenological constraints are systematically associated variational constraints, which need to be imposed on the variations considered in the principle. In this paper, by specifically focusing on the cases of simple thermodynamic systems with constraints, we show how the interconnections in thermodynamics can be also described by Dirac structures on the Pontryagin bundle as well as on the cotangent bundle of the thermodynamic configuration space. Each of these Dirac structures is induced from the variational constraint. Furthermore, the variational structure associated to this Dirac formulation is presented in the context of the Lagrange-dAlembert-Pontryagin principle. We illustrate our theory with some examples such as a cylinder-piston with ideal gas as well as an LCR circuit with entropy production due to a resistor.
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 structuring a dynamical syst
Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution equa- tion
In this paper, we present a Lagrangian formalism for nonequilibrium thermodynamics. This formalism is an extension of the Hamilton principle in classical mechanics that allows the inclusion of irreversible phenomena in both discrete and continuum sys
In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite dimensional case of discrete systems as well as for the infinite dimensional case of continuum systems. Starting with the funda
We analyze the relation of the notion of a pluri-Lagrangian system, which recently emerged in the theory of integrable systems, to the classical notion of variational symmetry, due to E. Noether. We treat classical mechanical systems and show that, f