  There is recent interest in determining energy costs of shortcuts to
adiabaticity (STA), but different definitions of "cost" have been used. We
demonstrate the importance of taking into account the Control System (CS) for a
fair assessment of energy flows and consumptions. We model the energy
consumption and power to transport an ion by a STA protocol in a multisegmented
Paul trap. The ion is driven by an externally controlled, moving harmonic
oscillator. Even if no net ion- energy is gained at destination, setting the
time-dependent control parameters is a macroscopic operation that costs energy
and results in energy dissipation for the short time scales implied by the
intrinsically fast STA processes. The potential minimum is displaced by
modulating the voltages on control (dc) electrodes. A secondary effect of the
modulation, usually ignored as it does not affect the ion dynamics, is the
time- dependent energy shift of the potential minimum. The non trivial part of
the energy consumption is due to the electromotive forces to set the electrode
voltages through the low-pass filters required to preserve the electronic noise
from decohering the ion's motion. The results for the macroscopic CS (the Paul
trap) are compared to the microscopic power and energy of the ion alone.
Similarities are found -and may be used quantitatively to minimize costs- only
when the CS-dependent energy shift of the harmonic oscillator is included in
the ion energy.
