A geometric perspective on Irreversible Thermodynamics. Part I: general concepts.

A new geometrical formulation of the thermodynamics of irreversible processes revisiting Coleman-Owen material point model has been proposed by the authors (in collaboration with P. Rogolino) a decade ago and since then applied by dierent teams of researchers to many dierent physical models in continuum thermodynamics such as viscoanelastic media, deformable dielectrics and magnetically polarizable undeformable media. The geometrical tools of contact/symplectic geometry were applied to introduce the Extended Thermodynamic Phase Space (ETPS) with its contact structure; in this space Legendre surfaces of equilibrium and Gibbs bundle have been constructed and the relations between the constitutive properties of continuum systems and the class of the entropy form have been discussed together with the introduction of the Hamiltonian formalism. The basic features of this geometrical formulation is here reviewed leaving the illustrations of relevant applications to part II of the present paper. The review is linked to a critical analysis focused on various open problems.