Certifying Quantum Signatures in Thermodynamics and Metrology via Contextuality of Quantum Linear Response

I 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 me to provide an example of a quantum engine whose favorable power output scaling unavoidably requires nonclassical effects in the form of contextuality. Furthermore, I describe contextual advantages for local metrology. Given the ubiquity of linear response theory, I anticipate that these tools will allow one to certify the nonclassicality of a wide array of quantum phenomena.