Relaxation in homogeneous and non-homogeneous polarized systems. A mesoscopic entropy approach

The dynamics of a degree of freedom associated to an axial vector in contact with a heat bath is described by means of a probability distribution function obeying a Fokker-Planck equation. The equation is derived by using mesoscopic non-equilibrium thermodynamics and permits a formulation of a dynamical theory for the axial degree of freedom (orientation, polarization) and its associated order parameter. The theory is used to describe dielectric relaxation in homogeneous and non-homogeneous systems in the presence of strong electric fields. In the homogeneous case, we obtain the dependence of the relaxation time on the external field as observed in experiments. In the non-homogeneous case, our model accounts for the two observed maxima of the dielectric loss giving a good quantitative description of experimental data at all frequencies, especially for systems with low molecular mass.