In the first technical lecture, I will use the tool box developed in treating time-dependent magnetoelectronic problems to consider a more general class of nonequilibrium phenomena in heterostructures with arbitrary spontaneous symmetry breaking. Motivated by the richness of physics in magnetic nanostructures, we are led to explore analogous phenomena in other symmetry-broken systems. As a first step in this direction, I will discuss a systematic way to construct “Archimedes screws” that are operated by semiclassical control of local orders. The “pumping” is achieved by means of a time-dependent order parameter which characterizes a broken symmetry and is controlled by external fields. The pumping itself is treated quantum-mechanically and the pumped quantity reflects the coherent condensate. I will illustrate the general theory by considering specific examples of helimagnet, superconducting, and density-wave orders and discuss experimental consequences, in close analogy with ferromagnetic spin pumping.