Thermodynamics of continuous media with permanent electric polarisation and magnetisation

The thermodynamics of an electrically charged, multicomponent fluid with permanent electric polarisation, permanent magnetisation and intrinsic vorticity is analysed in the presence of electromagnetic fields with magnetoelectric coupling in the classical limit. Three equations characterising the fluid are derived: a thermostatic equilibrium equation, a reversible and an irreversible thermodynamic evolution equation. These equations are obtained by taking into account the first and second laws of thermodynamics, the chemical reactions, the second law of Newton in translation and in rotation, the local time evolution of the permanent polarisation and the permanent magnetisation, and Maxwell's equations. Explicit expressions for the temperature and the chemical potentials are derived in terms of the electromagnetic fields, the permanent electric polarisation, the permanent magnetisation, the intrinsic vorticity and the magnetoelectric coupling. The analysis of the irreversible thermodynamics yields novel dissipative equations accounting in particular for dielectrophoresis, magnetophoresis, the relaxation of the permanent electric polarisation and the permanent magnetisation, and other properties of electrorheological and magnetorheological fluids.