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The Duality in Quantum Work

An open question of fundamental importance in quantum thermodynamics is how to describe the statistics of work for initial state with quantum coherence. In this paper, work statistics is considered from a fully new perspective of "wave-particle" duality. Based on the generalized quantum work measurement, predictability of energy levels $\mathcal{D}_W$ and effectiveness of coherence $\mathcal{V}_W$ are defined, and they obey inequality $\mathcal{D}_W^2+\mathcal{V}_W^2\leq1$, which is the fundamental tradeoff relations between the contributions of population and coherence to quantum work distribution. As an application, we consider a driven two-level system and discuss the condition of the bound of above tradeoff relation. These results shed light on the effects of quantum coherence in quantum thermodynamics.