A truly quantum Szil\'ard demon

We revisit the question of quantumness of thermal machines from a quantum information point of view. As an example we choose a one-qubit Szilard engine and ask when it can be considered to be truly quantum in the sense that the work output of the engine cannot be described by classical statistics. A truly quantum demon can exploit the correlations between the work medium and the surrounding bath. We will formulate the problem as a semi-device independent test which leads to a quantum steering scenario. While in a classical Szilard engine an objective description of the medium always exists, any such description can be ruled out by a steering task in the true quantum case.