  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- tions for nonequilibrium thermodynamics admit an intrinsic
formulation in terms of Dirac structures, both on the Lagrangian and the
Hamiltonian settings. In absence of irreversible processes these Dirac
structures reduce to canonical Dirac structures associated to canonical
symplectic forms on phase spaces. Our geometric formulation of nonequilibrium
thermodynamic thus consistently extends the geometric formulation of mechanics,
to which it reduces in absence of irreversible processes. The Dirac structures
are associated to the variational formulation of nonequilibrium thermodynamics
developed in Gay-Balmaz and Yoshimura [2016a,b] and are induced from a
nonlinear nonholonomic constraint given by the expression of the entropy
production of the system.
