MATERIAL ELEMENT MODEL AND DISSIPATIVE PROCESSES FOR FERRIMAGNETIC CRYSTALS WITH A NON-EUCLIDEAN STRUCTURE
Abstract
In a previous paper we outlined a geometric model for the thermodynamical description of ferrimagnetic crystals with a non-Euclidean structure. Applying a geometrization technique based on a model for magnetizable deformable media earlier introduced by Maugin, starting from an appropriate dynamical system on the fiber bundle of processes for simple material elements of these media, the expressions of the entropy function and the entropy 1-form were obtained. In this contribution we deepen the study of this geometrical model. We give a detailed description of the media under consideration, we introduce the transformation induced by the process and, applying the closure conditions for the entropy 1-form, we work out the necessary conditions for the existence of the entropy function. The derivation of the entropy 1-form is the starting point to introduce an extended thermodynamical phase space. Finally, from the exploitation of the Clausius–Duhem inequality, we derive, using Maugin's techniques, the residual dissipation inequality and the heat equation in the first and second form.
