Thermodynamics of ferromagnetic crystals

In a previous paper we have sketched a geometrical model for ferromagnetic crystals within a geometrized framework of simple materials with internal variables. Using a model of magnetizable media investigated by Maugin and coworkers, in the state vector the magnetization vector together with its space gradient (subjected to an evolution equation depending on both internal and external magnetic field) were included. In this paper we deepen the study of this geometrical model. In particular, from the exploitation of Clausius–Duhem inequality the entropy production and the state laws are calculated explicitly and starting from one appropriate dynamical system the expression for the entropy function and necessary conditions for its existence are got. Finally, using a Maugin's technique, the heat equation in the first and second form is derived.