Quantum Cycle in Relativistic Non-Commutative Space with Generalized Uncertainty Principle correction

TL;DR

This paper investigates how non-commutative spacetime and generalized uncertainty principle corrections influence the efficiency of quantum heat engines, finding efficiency boosts for harmonic oscillators but constant efficiency for infinite potential wells.

Contribution

It introduces the analysis of quantum heat engine efficiency in non-commutative relativistic space with GUP corrections, revealing catalytic effects on efficiency.

Findings

Efficiency increases with non-commutative parameter for harmonic oscillator

Efficiency remains constant in non-commutative space for infinite potential well

Non-commutative effects can enhance quantum engine performance

Abstract

Quantum heat cycles and quantum refrigerators are analyzed using various quantum systems as their working mediums. For example, to evaluate the efficiency and the work done of the Carnot cycle in the quantum regime, one can consider the harmonic oscillator as it's working medium. For all these well-defined working substances (which are analyzed in commutative space structure), the efficiency of the engine is not up to the mark of the Carnot efficiency. So, one inevitable question arise, can one observe a catalytic effect on the efficiency of the engines and refrigerators when the space structure is changed? In this paper, two different working substance in non-commutative spacetime with relativistic and generalized uncertainty principle corrections has been considered for the analysis of the efficiency of the heat engine cycles. The efficiency of the quantum heat engine gets a boost for higher values of the non-commutative parameter with a harmonic oscillator as the working substance. In the case of the second working medium (one-dimensional infinite potential well), the efficiency shows a constant result in the non-commutative space structure.