= Thermoelasticity with a temperature-dependent constraint
{title2=$\phi(F)=h(\theta)$}
The admissible rates obey $\phi_{,F}:\dot F=h'(\theta)\dot\theta$. A reaction multiplier $q$ in the reversible <nominal stress tensor> therefore has an accompanying <specific entropy> contribution:
$$
P_{Ii}=\rho_0\psi_{,F_{iI}}+q\phi_{,F_{iI}},\qquad\eta=-\psi_{,\theta}+\frac{q}{\rho_0}h'(\theta).
$$
Their reaction contributions cancel in the <Clausius-Duhem inequality> on admissible rates. Omitting the entropy term would generally violate the constraint's power balance.
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