On the non equilibrium thermodynamics and dynamics of a deformable interface between two electro-magnetically controllable fluids

media, both of them being magnetizable. The first part concerns the establishment of a complete set of dynamical equations allowing a complete description of the non equilibrium phenomena including a coupling between the internal angular momentum and the electromagnetic field. The effects of the relaxation processes are also discussed. We show that the deformation of the interface introduces a nonlinear term, proportional to the mean curvature, in

the surface dynamical equations of mass momentum and angular momentum. That term

intervenes also in the singular magnetic and electric fields inside the interface which lead to

the influence of currents and charge densities at the interface. In a second part, we give the expression

for the entropy production inside the interface as well as in the bulk phase. Using the general principles of non equilibrium thermodynamics, we compute the different thermodynamical fluxes.