In this study, we consider the quantum Szilárd engine with a single particle under the fractional power-law potential. We suggest that such kind of the Szilárd engine works a Stirling-like cycle. We obtain energy eigenvalues and canonical partition functions for the degenerate and non-degenerate cases in this cycle process. By using these quantities we numerically compute work and efficiency for this thermodynamic cycle for various power-law potentials with integer and non-integer exponents. We show that the presented simple engine also yields positive work and efficiency. We discuss the importance of fractional dynamics in physics and finally, we conclude that fractional calculus should be included in the fields of quantum information and thermodynamics.

在这项研究中，我们考虑分数幂律势下具有单个粒子的量子Szilárd引擎。我们建议这种Szilárd发动机采用类似斯特林的循环。在此循环过程中，我们获得了退化和非退化情况的能量特征值和规范划分函数。通过使用这些量，我们可以对具有整数和非整数指数的各种幂律电势的该热力学循环进行数值计算。我们表明，提出的简单引擎还可以产生积极的工作和效率。我们讨论了分数动力学在物理学中的重要性，最后得出结论，分数微积分应包含在量子信息和热力学领域。