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and thereby to the heating rate, 

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in virtue of Eq.(31). Employing Eqs.(29) and (33), we find that the magnetic relaxation transport coefficient in the magnetostriction model 

The Gilbert damping tensor follows from Eqs.(19) and (34) as 

The central relaxation tensor Eq.(35) describes the mag- netic relaxation in terms of the magnetostriction coeffi- cients and the crystal viscosity. 

From the electrostriction Eq.(14), it follows that a time varying polarization gives rise to a time varying strain 

and thereby to the heating rate, 

in virtue of Eq.(31). Employing Eqs.(30) and (37), we find that the electric relaxation transport coefficient in the electroostriction model 

The central relaxation tensor Eq.(38) describes the polar- ization relaxation time tensor coefficients in terms of the electrostriction coefficients and the crystal viscosity. The implications of the electrostriction model for the Landau- Khalatnikov equation is to the authors knowledge a new result. 

For ordered polarized and magnetized systems, we have developed phenomenological equations of motion in 

1 S. Machlup and L. Onsager, Phys. Rev. 91 , 1505 (1953). 2 

S. Machlup and L. Onsager, Phys. Rev. 91 , 1512 (1953). 3 

H.B. Callen, Fluctuation, Relaxation, and Resonance in 

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## B. Relaxation via Electrostriction 

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## V. CONCLUSIONS 

close analogy with one another. For the magnetized case, the relaxation is driven by the magnetic intensity H$_{d}$ yielding the Gilbert equation of motion $^{7}$. For the polar- ized case, the relaxation is driven by the electric field E$_{d}$ yielding the Tani equation of motion $^{17}$. In both cases, the relaxation time tensor τ is determined by the crystal viscosity as derived in the Appendix A; i.e. in Eqs.(A3) and (A6). The viscosity can be measured independently from the magnetic or electrical relaxation by employing sound absorption techniques $^{36}$. 

From the thermodynamic Eq.(10), the fluctuations in the magnetic intensity are given by magnetostriction, i.e. 

Eqs.(A1), (1) and (5) imply 

Employing Eqs.(A2), (2) and (6), one finds the central result for the magnetic relaxation time tensor; It is 

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From the thermodynamic Eq.(14), the fluctuations in the electric intensity are given by electrostriction, i.e. 

Eqs.(A4), (1) and (5) imply 

Employing Eqs.(A5), (2) and (6), one finds the central result for the electric relaxation time tensor; It is 

Magnetic Systems , Editor D. ter Haar, p 176, Oliver & Boyd Ltd., London (1962). 

4 R. Kubo, M. Toda and N. Hashitsume, Statistical Physics 

## Appendix A: Kubo formulae 

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