  A shortcut to adiabaticity is a driving protocol that reproduces in a short
time the same final state that would result from an adiabatic, infinitely slow
process. A powerful technique to engineer such shortcuts relies on the use of
auxiliary counterdiabatic fields. Determining the explicit form of the required
fields has generally proven to be complicated. We present explicit
counterdiabatic driving protocols for scale-invariant dynamical processes,
which describe for instance expansion and transport. To this end, we use the
formalism of generating functions, and unify previous approaches independently
developed in classical and quantum studies. The resulting framework is applied
to the design of shortcuts to adiabaticity for a large class of classical and
quantum, single-particle, non-linear, and many-body systems.
