Thermodynamics of ferromagnetic crystals with a non-Euclidean structure as internal variable

In this paper we construct a geometric model for deformable magnetizable bodies in the framework of thermodynamics of simple materials, taking into account a Maugin's approach for ferromagnetic crystals, developed within the irreversible thermodynamics with vectorial and tensorial internal variables. We explicitly consider an internal (non-Euclidean) metric as a thermodynamical non-equilibrium variable obtaining the dynamical system on the bre bundle of processes for simple material elements of the media under consideration. The derivation of this system is the first step to apply the qualitative theory of dynamical systems. Furthermore, we work out the entropy function and the entropy 1-form, which represents the starting point to introduce an extended thermodynamical phase space. Finally, from Clausius-Duhem inequality we give the extra-entropy flux and the state laws.