Quantum Stirling Heat Engine Based on the XY Heisenberg Spin Model in Tsallis Formalism

We study a quantum Stirling heat engine whose working substance is modeled by an anisotropic XY Heisenberg spin- 1 2 system. The thermodynamic properties of the engine are analyzed within the framework of Tsallis nonextensive statistics, where the generalized entropy 𝑆𝑞 accounts for long-range correlations and non-Markovian memory effects. Analytical expressions for internal energy and entropy are derived to compute work output and efficiency under various parameter regimes. Our findings reveal that, under moderate magnetic fields and realistic interaction asymmetries, the engine achieves non-negligible positive work and enhanced thermal efficiency in the subextensive regime (𝑞 < 1). A key feature of our model is the coupling-driven nature of the Stirling cycle, wherein thermodynamic processes are controlled by modulating the exchange interactions 𝐽𝐴 and 𝐽𝐵. These results demonstrate that the Tsallis parameter 𝑞 significantly influences thermodynamic performance, offering a viable pathway toward optimizing quantum thermal machines in strongly correlated, low-dimensional systems.