Abstract
In this paper, we show that the evolution equations for nonequilibrium thermodynamics can be formulated in terms of Dirac structures on the Pontryagin bundle \(\mathsf {P} =T \mathsf {Q}\oplus T ^* \mathsf {Q} \), where \(\mathsf {Q}=Q \times \mathbb {R}\) denotes the thermodynamic configuration manifold. In particular, we extend the use of Dirac structures from the case of linear nonholonomic constraints to the case of nonlinear nonholonomic constraints. Such a nonlinear constraint comes from the entropy production associated with irreversible processes in nonequilibrium thermodynamics. We also develop the induced Dirac structure on \(N=T^*Q \times \mathbb {R} \) and the associated Lagrange-Dirac and Hamilton-Dirac dynamical formulations.
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