Autonomous quantum thermodynamics with a quantum kicked top reservoir

We develop an operational framework to characterize energy exchange between a quantum system and a finite, dynamically tunable environment modeled by a quantum kicked top. Instead of relying on external driving or equilibrium assumptions, heat and work are defined through a weighted decomposition of the reservoir energy change, where the weighting factor quantifies the degree of thermalization based on long-time fluctuations. This approach provides a continuous interpolation between coherent (worklike) and incoherent (heatlike) energy transfer in finite quantum systems. By tuning the dynamical regime of the quantum kicked top from regular to chaotic, we show that increasing chaos enhances effective thermalization and converts structured energy flow into stochastic behavior. As an illustration, we consider an Otto-like energy conversion protocol. We demonstrate that both the apparent efficiency and fluctuations depend sensitively on the reservoir dynamics. This example highlights how partial thermalization can act as a resource while emphasizing that the resulting efficiency is an operational quantity rather than a thermodynamic bound.