 Dissipation potential

A dissipation potential is a function used to generate dissipative rates or their conjugate driving forces. In a force-based convention, a potential $\Phi (X)$ specifies an internal variable rate through $\dot{\alpha }={\partial }_X\Phi$. For example, $\Phi =X^2/(2\eta )$ with $\eta >0$ gives $\dot{\alpha }=X/\eta$ and dissipation $X\dot{\alpha }=X^2/\eta \ge 0$.

If $\Phi$ is differentiable and convex with a minimum at $X=0$, the convexity inequality gives $X{\partial }_X\Phi \ge \Phi (X)-\Phi (0)\ge 0$. This supplies a direct route to nonnegative dissipation. A rate-based convention instead generates forces from rates, so its variables must be stated explicitly. The potential is useful for organizing constitutive equations, but the complete model must still satisfy the Clausius-Duhem inequality, including thermal terms and the chosen energetic sign convention.