Thermodynamic speed limit for non-adiabatic work and its classical-quantum decomposition

Understanding the fundamental constraint on work far beyond the adiabatic regime is crucial to investigating fast and efficient energy extraction or consumption processes. In this study, we derive thermodynamic speed limits for non-adiabatic work and quantify the fundamental costs of non-adiabatic work extraction or consumption processes in open quantum systems, where the costs are quantified by geometric and thermodynamic quantities. We further decompose the non-adiabatic work into classical and quantum contributions and derive their thermodynamic speed limits, clarifying the classical and quantum nature of the fundamental costs. The obtained results are numerically demonstrated by driven two-level systems.