  The design of polycrystalline alloys hinges on a predictive understanding of
the interaction between the diffusing solutes and the motion of the constituent
crystalline interfaces. Existing frameworks ignore the dynamic multiplicity of
and transitions between the interfacial structures and phases. Here, we develop
a computationally-accessible theoretical framework based on short-time
equilibrium fluctuations to extract the drag force exerted by the segregating
solute cloud. Using three distinct classes of computational techniques, we show
that the random walk of a solute-loaded interface is necessarily non-classical
at short time-scales as it occurs within a confining solute cloud. The much
slower stochastic evolution of the cloud allows us to approximate the
short-time behavior as an exponentially sub-diffusive Brownian motion in an
external trapping potential with a stiffness set by the average drag force. At
longer time-scales, the interfacial and bulk forces lead to a gradual recovery
of classical random walk of the interface with a diffusivity set by the
extrinsic mobility. The short-time response is accessible via {\it ab-initio}
computations, offering a firm foundation for high throughput, rational design
of alloys for controlling microstructural evolution in polycrystals, and in
particular for nanocrystalline alloys-by-design.
