Non-commutative space: boon or bane for quantum engines and refrigerators

Abstract

Various quantum systems are considered as the working substance for the analysis of quantum heat cycles and quantum refrigerators. For example, one can consider harmonic oscillator as a working substance for the Carnot cycle to evaluate the efficiency and work of the engine. Even one can explore the coefficient of performance for the refrigerators by implementing a harmonic oscillator as a working substance for different cycles. However, for all these methods the efficiency of the engines cannot exceed the Carnot efficiency. So, a question arises whether a change in the space structure can provide any boost for the quantum engines and the refrigerators. Here, in this paper, we have studied the efficiency of the heat engine cycle and the coefficient of performance of the refrigerator cycles in the non-commutative space. The efficiency of the quantum heat engines gets a boost with the change in the space structure than the traditional quantum heat engine but the effectiveness of the noncommutative parameter is less for the efficiency compared to the coefficient of performance of the refrigerator. There is a steep boost for the coefficient of performance of the refrigerator cycles for the non-commutative space a harmonic oscillator compared to the harmonic oscillator.

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

“…The gain in the efficiency of he engine is provided by the relativistic correction. This is quite surprising as we have encountered gain due to the non-commutative parameters as shown in previous works [34][35][36][37]. This feature of suppressing the noncommutative affect with relativistic correction needs further investigation.…”