... Modified1
This form reduces to the classical Fick's law under special circumstances as described later .
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... potential.2
If this is to be generalized to non-conserved quantities, then another term is included to account for the local production of that non-conserved quantity,

$\displaystyle T \dot{\sigma} = -\frac{\ensuremath{\vec{J}}_Q}{T} \cdot \nabla T - \ensuremath{\vec{J}}_i \cdot \nabla F_i -{\cal P}(A)$ (03-3)

where $ {\cal P}(A)$ is a positive definite operator, e.g.,

$\displaystyle T \dot{\sigma} = -\frac{\ensuremath{\vec{J}}_Q}{T} \cdot \nabla T - \ensuremath{\vec{J}}_i \cdot \nabla F_i - \alpha A \dot{A}$ (03-4)

$\displaystyle T \dot{\sigma} = -\frac{\ensuremath{\vec{J}}_Q}{T} \cdot \nabla T - \ensuremath{\vec{J}}_i \cdot \nabla F_i - \frac{\alpha}{2} \dot{A^2}$ (03-5)

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