  Ratchets are devices able to rectify an otherwise oscillatory behavior by
exploiting an asymmetry of the system. In rocking ratchets the asymmetry is
induced through a proper choice of external forces and modulations of nonlinear
symmetric potentials. The ratchet currents thus obtained in systems as
different as semiconductors, Josephson junctions, optical lattices, or
ferrofluids, show a set of universal features. A satisfactory explanation for
them has challenged theorist for decades, and so far we still lack a general
theory of this phenomenon. Here we provide such a theory by exploring
---through functional analysis--- the constraints that the simple assumption of
time-shift invariance of the ratchet current imposes on its dependence on the
external drivings. Because the derivation is based on so general a principle,
the resulting expression is valid irrespective of the details and the nature of
the physical systems to which it is applied, and of whether they are classical,
quantum, or stochastic. The theory also explains deviations observed from
universality under special conditions, and allows to make predictions of
phenomena not yet observed in any experiment or simulation.
