On dielectric and magnetic relaxation phenomena and vectorial internal degrees of freedom in thermodynamics

It has been shown by the author in a previous paper that thermodynamic vectorial internal degrees of freedom which influence the polarization or the magnetization of a medium may give rise to dielectric or magnetic relaxation phenomena. Snoek's equation for magnetic relaxation phenomena was derived and it was shown that Debye's theory for dielectric after-effects in polar liquids is a special case of the developed theory. In this paper it is shown that if Z is some vectorial internal degree of freedom which influences the polarization a new internal degree of freedom bip^(int) may be defined which is a function of biZ, which may replace biZ as vectorial internal degree of freedom and which is a part of the total specific polarization. Furthermore, p^(int) may be introduced in such a way that the remaining part of the polarization, p^(el) (defined by $\text{p}{}^{\mathrm{<mtext>(</mtext><mtext>el</mtext><mtext>)</mtext>}}\text{=}\text{p}\text{?}\text{p}{}^{\mathrm{<mtext>int</mtext><mtext>)</mtext>}}$, where p is the total polarization per unit of mass), has the property that it vanishes for all values of p^(int) if the medium is in a state where the electric field E and the mechanical elastic stresses vanish and the temperature of the medium equals some reference temperature. If the equations of state are linearized the latter result implies for an isotropic medium $\text{E}\text{=ρa}{}^{\mathrm{(0,0)}}{}_{\mathrm{(bdp)}}\text{p}{}^{\mathrm{<mtext>(</mtext><mtext>el</mtext><mtext>)</mtext>}}$, where ρ is the mass density and a^(0,0)_(P) a constant. On the other hand p^(int) satifies a relaxation equation. It is seen that the use of p^(int) as an internal degree of freedom is of great advantage. This is connected with the fact that p^(int) is a measurable quantity in contradistinction to an arbitrary “hidden” vectorial internal degree of freedom. Analogous results may be obtained for magnetic after-effects.