  A central goal of thermodynamics is to identify optimal processes during
which the least amount of energy is dissipated into the environment. Generally,
even for simple systems, such as the parametric harmonic oscillator, optimal
control strategies are mathematically involved, and contain peculiar and
counter-intuitive features. We show that optimal driving protocols determined
by means of linear response theory exhibit the same step and $\delta$-peak like
structures that were previously found from solving the full optimal control
problem. However, our method is significantly less involved, since only a
minimum of a quadratic form has to be determined. In addition, our findings
suggest that optimal protocols from linear response theory are applicable far
outside their actual range of validity.
