Quantumness speeds up quantum thermodynamics processes

Quantum thermodynamic process involves manipulating and controlling quantum states to extract energy or perform computational tasks with high efficiency. There is still no efficient general method to theoretically quantify the effect of the quantumness of coherence and entanglement in work extraction. In this work, we propose a thermodynamics speed to quantify the extracting work. We show that the coherence of quantum systems can speed up work extracting with respect to some cyclic evolution beyond all incoherent states. We further show the genuine entanglement of quantum systems may speed up work extracting beyond any bi-separable states. This provides a new thermodynamic method to witness entangled systems with physical quantities.