This paper considers work extraction from a quantum system to a work storage system (or weight) following reference [1]. An alternative approach is here developed that relies on the comparison of subspace dimensions without a need to introduce thermo-majorisation used previously. Optimal single shot work for processes where a weight transfers from (a) a single energy level to another single energy level is then re-derived. In addition we discuss the final state of the system after work extraction and show that the system typically ends in its thermal state, while there are cases where the system is only close to it. The work of formation in the single level transfer setting [1] is also re-derived. The approach presented now allows the extension of the single shot work concept to work extraction (b) involving multiple final levels of the weight. A key conclusion here is that the single shot work for case (a) is appropriate only when a \emph{resonance} of a particular energy is required. When wishing to identify "work extraction" with finding the weight in a specific available energy or any higher energy a broadening of the single shot work concept is required. As a final contribution we consider transformations of the system that (c) result in general weight state transfers. Introducing a transfer-quantity allows us to formulate minimum requirements for transformations to be at all possible in a thermodynamic framework. We show that choosing the free energy difference of the weight as the transfer-quantity one recovers various single shot results including single level transitions (a), multiple final level transitions (b), and recent results on restricted sets of multi-level to multi-level weight transfers.
Operational Quasiprobability in Quantum Thermodynamics: Work Extraction by Coherence and Non-joint Measurability
Samsung SDS（三星SDS）；Korea Institute of Science and Technology Information (KISTI)（韩国科学技术信息研究所）；Korea University of Science and Technology（韩国科学技术院）；Kumoh National Institute of Technology（龟尾国立技术大学）
Experimental Extraction of Coherent Ergotropy and Its Energetic Cost in a Superconducting Qubit
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Hefei National Laboratory（合肥国家实验室）
Work extraction from long-lived quantum coherence of a three-level system
School of Physics, Xi'an Jiaotong University（西安交通大学物理学院）；MOE Key Laboratory for Non-equilibrium Synthesis and Modulation of Condensed Matter（教育部凝聚态物质非平衡合成与调制重点实验室）；Hefei National Laboratory（合肥国家实验室）
