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 efficientgeneral 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 theextracting work. We show that the coherence of quantum systems can speed up work extractingwith 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-separablestates. This provides a new thermodynamic method to witness entangled systems without statetomography.