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The driving magnetic intensity determines the torque on the magnetic moments according to 

Employing Eqs.(11) and (17), one finds the equations for magnetic resonance in the Gilbert form 

wherein the Gilbert dimensionless damping tensor α is defined as 

One may directly solve the Gilbert equations for the driv- ing magnetic intensity according to 

Eqs.(17) and (20) express the magnetic resonance motion in the Landau-Lifshitz form. 

The driving electric field gives rise to a polarization response according to 

wherein ω$_{p}$ is the plasma frequency. A simple derivation of Eq.(21) may be formulated as follows. In a large vol- ume V , the polarization due to charges { z$_{j}$e } is given by 

If the driving electric field accelerates the charges accord- ing to 

then Eq.(21) holds true with the plasma frequency 

wherein n$_{a}$ is the density of charged particles of type a . 

The polarization resonance equation of motion follows from Eqs.(16) and (21) as 17 

## A. Gilbert-Landau-Lifshitz Equations 

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## B. Landau-Khalatnikov-Tani Equations 

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The electric field E induces the polarization P at reso- nant frequencies which are eigenvalues of the tensor Ω for which 

The decay rates for the polarization oscillations are eigen- values of the tensor Γ for which 

If the decay rates are large on the scale of the the resonant frequencies, then the equation of motion is over damped so that 

Eq.(28) represents the Landau-Khalatnikov equation for polarized systems. 

## IV. HEATING RATE PER UNIT VOLUME 

Let us here consider the heating rate implicit in relax- ation processes. Independently of the details of the mi- croscopic mechanism for generating such heat, the rates of energy dissipation are entirely determined by τ . Ex- plicitly, the heating rates per unit volume for magnetiza- tion and polarization are given, respectively, by 

and 

Finally, the notion of crystal viscosity η$_{ijkl}$ is introduced into elasticity theory 35 via the heating rate per unit vol- ume from rates of change in the strain ∂ e /∂t ; It is 

Crystal viscosity is employed to describe, among other things, sound wave attenuation. Our purpose is to de- scribe how heating rates in Eqs.(29) and (30) can be re- lated to the heating rate in Eq.((31)). This allows us to express the transport coefficients τ in terms of the crystal viscosity. 

## A. Relaxation via Magnetostriction 

From the magnetostriction Eq.(10), it follows that magnetic relaxation gives rise to a strain 

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