Quantum Szilard engine for the fractional power-law potentials

In this study, we consider the quantum Szilard engine with a single particle under the fractional power-law potential. We suggest that such kind of the Szilard 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.

Automated summary

This study investigates the quantum Szilard engine operating under a fractional power-law potential, proposing that it works in a Stirling-like cycle. Numerical computations of work and efficiency for various power-law potentials reveal positive results, indicating the potential of this simple engine. The discussion highlights the significance of fractional dynamics in physics and suggests the inclusion of fractional calculus in the fields of quantum information and thermodynamics.