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

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Abstract

Various quantum systems are considered as the working substance for the analysis of quantum heat cycles and quantum refrigerators. The ongoing technological challenge is how efficiently can a heat engine convert thermal energy to mechanical work. The seminal work of Carnot has proposed a fundamental upper limit—the Carnot limit on the efficiency of the heat engine. However, the heat engines can be operated beyond the fundamental upper limit by exploiting non-equilibrium reservoirs. Here, the change in the space structure introduces the non-equilibrium effect. So, a question arises whether a change in the space structure can provide any boost for the quantum engines and refrigerators. The efficiency of the heat cycle and the coefficient of performance (COP) of the refrigerator cycles in the non-commutative space are analyzed here. 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 non-commutative parameter is less for the efficiency compared to the COP of the refrigerator. There is a steep boost for the coefficient of performance of the refrigerator cycles for the non-commutative space harmonic oscillator compared to the harmonic oscillator.

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Acknowledgements

The author gratefully acknowledges for the useful discussions and suggestions from Dr. Goutam Paul, Associate Prof. of Cryptology and Security Research Unit, R.C. Bose Center for Cryptology and Security, at Indian Statistical Institute, Kolkata and Mr. Tanmoy Pandit of Hebrew University of Jerusalem, Jerusalem, Israel. We thank the reviewer for constructive comments.

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Authors and Affiliations

  1. Cryptology and Security Research Unit, R.C. Bose Center for Cryptology and Security, Indian Statistical Institute, Kolkata, 700108, India

    Pritam Chattopadhyay

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Correspondence to Pritam Chattopadhyay.

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Chattopadhyay, P. Non-commutative space: boon or bane for quantum engines and refrigerators. Eur. Phys. J. Plus 135, 302 (2020). https://doi.org/10.1140/epjp/s13360-020-00318-7

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