  We identify a fundamental difference between classical and quantum dynamics
in the linear response regime by showing that the latter is in general
contextual. This allows us to provide an example of a quantum engine whose
favorable power output scaling \emph{unavoidably} requires nonclassical effects
in the form of contextuality. Furthermore, we describe contextual advantages
for local metrology. Given the ubiquity of linear response theory, we
anticipate that these tools will allow one to certify the nonclassicality of a
wide array of quantum phenomena.
