Optimal performance of generalized heat engines with finite-size baths of arbitrary multiple conserved quantities beyond i.i.d. scaling

摘要

In quantum thermodynamics, effects of finiteness of the baths have been lessconsidered. In particular, there is no general theory which focuses onfiniteness of the baths of multiple conserved quantities. Then, we investigatehow the optimal performance of generalized heat engines with multiple conservedquantities alters in response to the size of the baths. In the context ofgeneral theories of quantum thermodynamics, the size of the baths has beengiven in terms of the number of identical copies of a system, which does notcover even such a natural scaling as the volume. In consideration of theasymptotic extensivity, we deal with a generic scaling of the baths tonaturally include the volume scaling. Based on it, we derive a bound for theperformance of generalized heat engines reflecting finite-size effects of thebaths, which we call fine-grained generalized Carnot bound. We also construct aprotocol to achieve the optimal performance of the engine given by this bound.Finally, applying the obtained general theory, we deal with simple examples ofgeneralized heat engines. As for an example of non-i.i.d.~scaling and multipleconserved quantities, we investigate a heat engine with two baths composed ofan ideal gas exchanging particles, where the volume scaling is applied. Theresult implies that the mass of the particle explicitly affects the performanceof this engine with finite-size baths.