Steering Heat Engines: A Truly Quantum Maxwell Demon

We address the question of verifying the quantumness of thermal machines. A Szil\'ard engine is truly quantum if its work output cannot be described by a local hidden state (LHS) model, i. e. an objective local statistical ensemble. Quantumness in this scenario is revealed by a steering-type inequality which bounds the classically extractable work. A quantum Maxwell demon can violate that inequality by exploiting quantum correlations between the...