Effects of State Degeneration in 3D Quantum Lenoir Engine Performance





quantum lenoir engine, single-particle, cubic potential, degenerate state, efficiency


We study the performance of the quantum Lenoir engine using single-particle confined within the cubic potential. In 3D potential structure, particles degenerate into multiple states at identic energy level which occurs on the excitation state of the particles. Deliberating the degeneration effects, the confined particle has possibility to produce more energy efficiency as engine’s working substance. The particle is able to freely move in three directions of x, y, and z-axis simultaneously, which gives three degrees of freedom to the particle in the cubic potential. By limiting to two eigen states, a basic explanation to the condition of the particle was provided. The efficiency of 3D quantum Lenoir engine is better than the classical model of the Lenoir engine despite the similarity in the formulation. Moreover, we also consider the efficiency comparison between the 3D model, with some state modifications, and the 1D efficiency of the quantum Lenoir engine. As expected, degeneration of the particle’s states plays a role in the enhancement of the quantum Lenoir engine’s efficiency. Moreover, we also derived the power output of the 3D quantum Lenoir engine. Thus, this study clearly gives a sight of the performance of quantum Lenoir engine model in the 3D manner.


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Author Biography

Trengginas E. P. Sutantyo, Universitas Andalas



Department of Physics, Andalas University, Padang, Indonesia  


Abdillah, F., & Saputra, Y. D. (2021). Quantum-Mechanical Brayton Engine based on a Boson Particle Inside Cubic Potential. Journal of Physics: Conference Series, 1726(1). DOI: https://doi.org/10.1088/1742-6596/1726/1/012004

Akbar, M. S., Latifah, E., & Wisodo, H. (2018). Limit of Relativistic Quantum Brayton Engine of Massless Boson Trapped 1 Dimensional Potential Well. Journal of Physics: Conference Series, 1093(1). DOI: https://doi.org/10.1088/1742-6596/1093/1/012031

Ali, Md. M., Huang, W.-M., & Zhang, W.-M. (2020). Quantum thermodynamics of single particle systems. Scientific Reports, 10(1), 13500. DOI: https://doi.org/10.1038/s41598-020-70450-y

Belfaqih, I. H., Sutantyo, T. E. P., Prayitno, T. B., & Sulaksono, A. (2015). Quantum-Carnot engine for particle confined to 2D symmetric potential well. AIP Conference Proceedings, 1677. DOI: https://doi.org/10.1063/1.4930654

Bender, C. M., Brody, D. C., & Meister, B. K. (2000). Quantum mechanical Carnot engine. Journal of Physics A: Mathematical and General, 33(24), 4427–4436. DOI: https://doi.org/10.1088/0305-4470/33/24/302

Fernández, J. J. (2022). Optimization of energy production in two-qubit heat engines using the ecological function. Quantum Science and Technology, 7(3), 035002. DOI: https://doi.org/10.1088/2058-9565/ac635a

Kieu, T. D. (2006). Quantum heat engines, the second law and Maxwell’s daemon. The European Physical Journal D, 39(1), 115–128. DOI: https://doi.org/10.1140/epjd/e2006-00075-5

Latifah, E., & Purwanto, A. (2013). Quantum Heat Engines; Multiple-State 1D Box System. Journal of Modern Physics, 04(08), 1091–1098. DOI: https://doi.org/10.4236/jmp.2013.48146

Muñoz, E., & Peña, F. J. (2012). Quantum heat engine in the relativistic limit: The case of a Dirac particle. Physical Review E, 86, 061108. DOI: https://doi.org/10.1103/PhysRevE.86.061108

Saputra, Y. D. (2021). Quantum Lenoir Engine with a Multiple-eigenstates Particle in 1D Potential Box. Journal of Physics: Conference Series, 1726(1). DOI: https://doi.org/10.1088/1742-6596/1726/1/012016

Scovil, H. E. D., & Schulz-DuBois, E. O. (1959). Three-Level Masers as Heat Engines. Physical Review Letters, 2(6), 262–263. DOI: https://doi.org/10.1103/PhysRevLett.2.262

Singh, S. (2020). Quantum Brayton Engine of Non-Interacting Fermions in a One Dimensional Box. International Journal of Theoretical Physics, 59(9), 2889–2900. DOI: https://doi.org/10.1007/s10773-020-04549-3

Singh, S., & Rebari, S. (2020). Multi-level quantum diesel engine of non-interacting fermions in a one-dimensional box. The European Physical Journal B, 93(8), 150. DOI: https://doi.org/10.1140/epjb/e2020-10217-0

Sutantyo, T. E. P. (2020). Three-State Quantum Heat Engine Based on Carnot Cycle. Jurnal Fisika Unand, 9(1), 142–149. DOI: https://doi.org/10.25077/jfu.9.1.142-149.2020

Sutantyo, T. E. P., Belfaqih, I. H., & Prayitno, T. B. (2015). Quantum-Carnot engine for particle confined to cubic potential. AIP Conference Proceedings, 1677. DOI: https://doi.org/10.1063/1.4930655

Sutantyo, T. E. P., Fahriza, A., & Abdullah, Z. (2021). Optimizations of Multilevel Quantum Heat Engine with N Noninteracting Fermions Based on Lenoir Cycle. arXiv:2112.02904v2 [cond-mat. stat-mech].

Wang, J., & He, J. (2012). Optimization on a three-level heat engine working with two noninteracting fermions in a one-dimensional box trap. Journal of Applied Physics, 111(4). DOI: https://doi.org/10.1063/1.3681295

Yuan, H., Ma, Y.-H., & Sun, C. P. (2022). Optimizing thermodynamic cycles with two finite-sized reservoirs. Physical Review E, 105(2), L022101. DOI: https://doi.org/10.1103/PhysRevE.105.L022101

Zettili, N. (2009). Quantum Mechanics: concepts and applications (2nd ed.). John Wiley & Sons, Ltd.




How to Cite

Fahriza, A., & Sutantyo, T. E. P. (2022). Effects of State Degeneration in 3D Quantum Lenoir Engine Performance. Jurnal Ilmu Fisika, 14(2), 95–107. https://doi.org/10.25077/jif.14.2.95-107.2022



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