#### 9.6.3.1 The deformation-temperature-electric field-magnetic field formulation

In this formulation, F, Θ, e*, and h* are the independent variables. We define the energy potential E^{F}^{Θeh} as the Legendre transformation of internal energy $\epsilon =\stackrel{\u02d8}{\epsilon}\left(\mathbf{F},\eta ,{\mathbf{p}}^{*}/\rho ,{\mathbf{m}}^{*}/\rho \right)$ with respect to the thermal, electrical, and magnetic variables, from η to Θ, p*/ρ to e*, and m*/ρ to h*, i.e.,

${E}^{F\text{\Theta}\mathit{eh}}=\epsilon -\text{\Theta}\eta -{\mathbf{e}}^{*}\xb7\frac{{\mathbf{p}}^{*}}{\rho}-{\mu}_{\text{o}}{\mathbf{h}}^{*}\xb7\frac{{\mathbf{m}}^{*}}{\rho}.$

(9.71)

Refer to Table 9.4. Taking the rate of (9.71) gives

${\stackrel{.}{E}}^{F\text{\Theta}\mathit{eh}}=\stackrel{.}{\epsilon}-\text{\Theta}\stackrel{.}{\eta}-\eta \stackrel{.}{\text{\Theta}}-{\mathbf{e}}^{*}\xb7\stackrel{\xb7}{\overline{\left(\frac{{\mathbf{p}}^{*}}{\rho}\right)}}-\frac{{\mathbf{p}}^{*}}{\rho}\xb7{\stackrel{.}{\mathbf{e}}}^{*}-{\mu}_{\text{o}}{\mathbf{h}}^{*}\xb7\stackrel{\xb7}{\overline{\left(\frac{{\mathbf{m}}^{*}}{\rho}\right)}}-{\mu}_{\text{o}}\frac{{\mathbf{m}}^{*}}{\rho}\xb7{\stackrel{.}{\mathbf{h}}}^{*},$

and use of this result in (9.61 ...

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