Correlated quantum machines beyond the standard second law

The laws of thermodynamics strongly restrict the performance of thermal machines. Standard thermodynamics, initially developed for uncorrelated macroscopic systems, does not hold for microscopic systems correlated with their environments. We here derive an exact formula for the efficiency of any cyclically driven quantum engine by using generalized laws of quantum thermodynamics that account for all possible correlations between all involved parties, including initial correlations. Furthermore, we demonstrate the existence of two basic modes of engine operation: the usual thermal case, where heat is converted into work, and an athermal regime, where work is extracted from entropic resources, such as system-bath correlations. In the latter regime, the efficiency is not bounded by the usual Carnot formula. Our results provide a unified formalism to determine the efficiency of correlated microscopic quantum machines.