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arXiv:2602.04538

Thermodynamic Cost of Regeneration in a Quantum Stirling Cycle

Ferdi Altintas

quant-phSubmitted Feb 4, 2026• Announced Feb 5, 2026• 0 citations• Revised Apr 29, 2026 (v2)
v1 · Feb 4, 2026v2 · Apr 29, 2026
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Abstract

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.

Comments
Revised version; submitted to a journal

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ABSTRACT We investigate a quantum Stirling engine whose working medium is a three‐qubit Heisenberg XXZ spin chain incorporating the Dzyaloshinskii‐Moriya interaction. The integration of a regenerator, which recovers internal energy during the isochoric processes, significantly enhances the efficiency of the engine, allowing it to approach the Carnot efficiency under appropriate parameters. Our analysis reveals a pronounced stage dependence of quantum correlations: at the end of the isothermal expansion, quantum entanglement and coherence of the thermal equilibrium state are positively correlated with the cycle efficiency, whereas at the end of the isothermal compression, they are negatively correlated with the efficiency. Furthermore, we demonstrate how external magnetic fields and coupling coefficients regulate these quantum correlations and the engine performance, including the work output and efficiency. This work provides a systematic comparison of the stage‐dependent roles of entanglement and coherence in a three‐qubit Stirling cycle, offering insights for designing high‐performance regenerative quantum thermal devices.