We investigate the Stirling-cycle performance of a Heisenberg--Kitaev magnonic medium with Dzyaloshinskii--Moriya (DM) interactions. Using linear spin-wave theory, we show the DM interaction preserves spectral symmetry, yielding even caloric responses and symmetric Stirling engine efficiency. In contrast, bond-dependent Kitaev exchange asymmetrically distorts the magnonic density of states, enabling distinct direct and inverse caloric effects. Consequently, Kitaev-driven cycles achieve significantly higher efficiencies than DM-driven protocols, approaching a high-performance saturation regime for negative couplings. This establishes exchange-anisotropic magnets as highly tunable platforms for nanoscale solid-state energy conversion.
We study the standard four-stroke regenerative quantum Stirling heat engine cycle, which assumes local thermal equilibrium at each stage, within the standard weak-coupling, Markovian open quantum system framework. We point out that the regeneration process is not thermodynamically free in a reduced open-system description, and we treat the required work input as an explicit regeneration cost by modifying the cycle efficiency accordingly. We consider two working substances--a single spin-
1/2 and a pair of interacting spin-
1/2 particles--and investigate the cycle performance by taking the regeneration cost at its minimum value set by the Carnot heat-pump limit. For comparison, we also analyze the conventional Stirling cycle without regeneration under the same conditions. The super-Carnot efficiencies reported under the cost-free regeneration assumption disappear once the regeneration cost is included: the modified efficiency stays below the Carnot bound, while still remaining higher than the efficiency of the conventional Stirling cycle. For the conventional Stirling cycle, we provide a rigorous Carnot bound using quantum relative entropy, whereas for the regenerative cycle we derive a sufficient lower bound on the regeneration cost that guarantees thermodynamic consistency. Finally, we suggest three candidate quantum regenerator models for future work.