Coleman-Noll procedure
= Coleman-Noll procedure
{c}
Requiring the <Clausius-Duhem inequality> for independent reversible mechanical and thermal variations constrains a <constitutive equation>. For $U(F,\eta,\xi)$ it gives $P_{Ii}=\rho_0U_{,F_{iI}}$ and $\theta=U_{,\eta}$. Combining the <Lagrangian internal energy balance> with the <Lagrangian entropy inequality> leaves $f_r\dot\xi_r-q_I\theta_{,I}/\theta\ge0$. The independence assumptions are part of the constitutive argument.