Nonholonomic theory for dielectric relaxation phenomena in isotropic media

We discuss the dielectric relaxation phenomena from the point of view of nonholonomic irreversible thermodynamics. For that we introduce the space of states as a 39-dimensional manifold and we obtain the entropy as harmonic function via extremals of a least squares Lagrangian. If the theory is linearized, it appears like a dynamical constitutive equation (relaxation equation) based on a linear combination between the electric field E, the polarization P, the first derivatives with respect to time of E and P and the second derivative with respect to time of P. The Debye equation for dielectric relaxation in polar liquids as well as the De Groot–Mazur equation are special cases of such equation. These equations reflect the affine dependence between the pairs P and E, D and E. Using nonholonomic thermodynamic arguments, several inequalities are derived for the coefficients which occur in the relaxation equations.