MiS Preprint Repository

By applying linear response theory and the Onsager principle, the power (per unit area) needed to make a planar interface move with velocity $V$ is found to be equal to $V^2/\mu$, $\mu$ a mobility coefficient. To verify such a law, we study a one dimensional model where the interface is the stationary solution of a non local evolution equation, called an instanton. We then assign a penalty functional to orbits which deviate from solutions of the evolution equation and study the optimal way to displace the instanton. We find that the minimal penalty has the expression $V^2/\mu$ only when $V$ is small enough. Past a critical speed, there appear nucleations of the other phase ahead of the front, their number and location are identified in terms of the imposed speed.