Analytical shortcuts to adiabaticity of weakly driven processes

The analytical expression for shortcuts to adiabaticity for any switching time and any thermally isolated system performing a finite-time and weakly driven process is presented. It is based on the analytical solution of the optimal protocols of weak processes for open systems. The extension to adiabatic processes was made by employing the concept of waiting time. The shortcuts to adiabaticity are proven by showing that the excess power is null in all instants, indicating that no nonequilibrium excitation occurs along the driving. Two examples are solved to verify the validity of such shortcuts: the typical case of oscillatory relaxation function and the transverse-field quantum Ising chain. In this last case, it is shown that non-quenching process outperforms the quenching one by suppressing the non-equilibrium excitations until the critical point is not achieved.