The Duality in Quantum Work

Abstract: 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.