Transient energy excitation in shortcuts to adiabaticity for the time-dependent harmonic oscillator

We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes (shortcuts to adiabaticity) designed to reproduce the initial populations at some predetermined final frequency and time. We provide lower bounds and examples. Implications for the limits imposed to the process times and for the principle of unattainability of the absolute zero, in a single expansion or in quantum refrigerator cycles, are drawn.