Kinetic roughening, global quantities, and fluctuation–dissipation relations

Growth processes and interface fluctuations can be studied through the properties of global quantities. We here discuss a global quantity that not only captures better the roughness of an interface than the widely studied surface width, but that is also directly conjugate to an experimentally accessible parameter, thereby allowing us to study in a consistent way the global response of the system to a global change of external conditions. Exploiting the full analyticity of the linear Edwards–Wilkinson and Mullins–Herring equations, we study in detail various two-time functions related to that quantity. This quantity fulfills the fluctuation–dissipation theorem when considering steady-state equilibrium fluctuations.