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THERMODYNAMICS OF FERROMAGNETIC CRYSTALS

MAURO FRANCAVIGLIA

Department of Mathematics, University of Torino, Via Carlo Alberto 10, Turin 10123, Italy

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LILIANA RESTUCCIA

Department of Mathematics, University of Messina, Viale F. Stagno d'Alcontres 31, Messina 98166, Italy

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PATRIZIA ROGOLINO

Department of Mathematics, University of Messina, Viale F. Stagno d'Alcontres 31, Messina 98166, Italy

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https://doi.org/10.1142/S0219887812500648Cited by:1 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 74F15

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