Beyond the Carnot limit: work extraction via an entropy battery

Heat is a physical manifestation of entropy, where the removal of entropy from a thermal energy reservoir permits the conversion of heat into work. This entropy transfer is facilitated by the cold thermal energy reservoir in typical heat engines. Recent developments in quantum heat engines that operate between thermal energy and spin angular momentum reservoirs show that it is possible to transfer entropy out of energy and into a different conserved quantity. The implications of this type of entropy transfer have not been fully explored, especially on the work extractable using an ensemble with multiple conserved quantities. Using the aforementioned heat engines, we show that such an ensemble will transform heat into work beyond the Carnot efficiency limit while operating at maximum power. This result is obtained without induced quantum coherence, a technique commonly used in the field of quantum heat engines to achieve the same outcome. Without loss of generality, we also show that thermal spin reservoirs behave as thermodynamic baths with well-defined temperatures, heat capacities, and fluctuation-dissipation relations. Finally, our analysis of entropy capacity suggests that particle indistinguishability is necessary for inter-particle interactions, and for entropy to transfer between canonical ensembles. These results establish a foundation for entropy-based quantum devices that extract work from a hot thermal energy reservoir more efficiently than possible with a cold thermal energy reservoir. These devices also act as high energy-density batteries and efficient heat storage systems. Our results will have implications for quantum heat engines, spinor condenstates, spintronics, and quantum batteries.