Quantum Szilard engine for the fractional power-law potentials

Ekrem Aydiner

doi:10.1038/s41598-020-80639-w

Abstract

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.

Highlights

In this study, we consider the quantum Szilárd engine with a single particle under the fractional power-law potential
It is shown that the second law of thermodynamics will not be violated, if a more complete analysis is made of the whole system including the demon
It is clearly understood by these studies that there is a connection between thermodynamic entropy and information entropy which leads positive work

Summary

Introduction

We consider the quantum Szilárd engine with a single particle under the fractional power-law potential. Since the average kinetic energy of the particles will be interpreted as an expression of temperature, at the end of this process, this means that the temperature of box B increases, the temperature of box A decreases. If this thought experiment is possible, a heat transfer from cold to hot would be possible and this indicates that the second law can be violated.

Methods

Conclusion