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

Classical dissipative cost of quantum control