  Protocols for non-adiabatic quantum control often require the use of
classical time varying fields. Assessing the thermodynamic cost of such
protocols, however, is far from trivial. In this letter we study the
irreversible entropy produced by the classical apparatus generating the control
fields, thus providing a direct link between the cost of a control protocol and
dissipation. We focus, in particular, on the case of time-dependent magnetic
fields and shortcuts to adiabaticity. Our results are showcased with two
experimentally realisable case studies: the Landau-Zener model of a spin-1/2
particle in a magnetic field and an ion confined in a Penning trap.
