Dimensionality and geometry effects on a quantum carnot engine efficiency


  • Hiram Kalid Herrera Alcantar Faculty of Sciences, Autonomous University of Baja California, Ensenada, Baja California, Mexico
  • José Carlos Carvajal García Faculty of Sciences, Autonomous University of Baja California, Ensenada, Baja California, Mexico
  • Osvaldo Rosales Pérez Faculty of Sciences, Autonomous University of Baja California, Ensenada, Baja California, Mexico
  • Rubén Cesar Villarreal-Sánchez Faculty of Engineering, Architecture and Design, Autonomous University of Baja California, Ensenada-Tijuana 3917 transpeninsular highway, Playitas neighborhood, Ensenada, Baja California, Mexico https://orcid.org/0000-0002-5395-580X
  • Priscilla Elizabeth Iglesias-Vázquez Faculty of Sciences, Autonomous University of Baja California, Ensenada, Baja California, Mexico




Carnot cycle, Heat engine, Quantum confinement.


We calculate the efficiency of a quantum Carnot cycle for a particle confined in two different infinite potential wells, a cylindrical potential well of variable radius and a two-dimensional square potential well with a periodicity in one of it sides. We find that the efficiency depends directly on the dimensionality and geometry of the well that confined the particle.


Download data is not yet available.


Metrics Loading ...


S. Carnot, “Réflexions sur la puissance motrice du feu”. Paris, Annales scientifiques de l’É.N.S. 2e série, tome 1, p. 393-457, 1872. http://www.numdam.org/item?id=ASENS_1872_2_1__393_0 DOI: https://doi.org/10.24033/asens.88

J. E. Geusic, E. O. Schulz-DuBios, and H. E. D. Scovil, “Quantum equivalent of the Carnot cycle,” Phys. Rev., vol. 156(2), pp. 343. 1967. https://doi.org/10.1103/PhysRev.156.343 DOI: https://doi.org/10.1103/PhysRev.156.343

C. M. Bender, D. C. Brody, and B. K. Meister, “Quantum mechanical Carnot engine,” J. Phys. A. Math. Gen., vol. 33, no. 24, pp. 4427–4436, 2000. https://doi.org/10.1088/0305-4470/33/24/302 DOI: https://doi.org/10.1088/0305-4470/33/24/302

H. T. Quan, Y. Liu, C. P. Sun, and F. Nori, “Quantum thermodynamic cycles and quantum heat engines,” Phys. Rev. E, vol. 76, no. 3, p. 31105, Sep. 2007. https://doi.org/10.1103/PhysRevE.76.031105 DOI: https://doi.org/10.1103/PhysRevE.76.031105

H. T. Quan, “Quantum thermodynamic cycles and quantum heat engines. II.,” Phys. Rev. E, vol. 79, no. 4, p. 41129, 2009. https://doi.org/10.1103/PhysRevE.79.041129 DOI: https://doi.org/10.1103/PhysRevE.79.041129

T. D. Kieu, “The second law, Maxwell's demon, and work derivable from quantum heat engines,” Phys. Rev. Lett., vol. 93(14), pp.140403. 2004. https://doi.org/10.1103/PhysRevLett.93.140403 DOI: https://doi.org/10.1103/PhysRevLett.93.140403

S. Abe and S. Okuyama, “Similarity between quantum mechanics and thermodynamics: Entropy, temperature, and Carnot cycle,” Phys. Rev. E, vol. 83, no. 2, p. 21121, Feb. 2011. https://doi.org/10.1103/PhysRevE.83.021121 DOI: https://doi.org/10.1103/PhysRevE.83.021121

J. Wang, J. He, and Z. Wu, “Efficiency at maximum power output of quantum heat engines under finite-time operation,” Phys. Rev. E, vol. 85, no. 3, p. 31145, Mar. 2012. https://doi.org/10.1103/PhysRevE.85.031145 DOI: https://doi.org/10.1103/PhysRevE.85.031145

S. Abe, “General formula for the efficiency of quantum-mechanical analog of the Carnot engine,” Entropy, vol. 15(4), pp. 1408. 2013. https://doi.org/10.3390/e15041408 DOI: https://doi.org/10.3390/e15041408

B. Zwiebach, A First Course in String Theory, 2nd ed. Cambridge: Cambridge University Press, 2009. https://doi.org/10.1017/CBO9780511841620 DOI: https://doi.org/10.1017/CBO9780511841620

P. P. Hofer, J.-R. Souquet, and A. A. Clerk, “Quantum heat engine based on photon-assisted Cooper pair tunneling,” Phys. Rev. B, vol. 93, no. 4, p. 41418, 2016. https://doi.org/10.1103/PhysRevB.93.041418 DOI: https://doi.org/10.1103/PhysRevB.93.041418

P. P. Hofer, J. B. Brask, M. Perarnau-Llobet, and N. Brunner, “Quantum Thermal Machine as a Thermometer,” Phys. Rev. Lett., vol. 119, no. 9, p. 90603, Sep. 2017. https://doi.org/10.1103/PhysRevLett.119.090603 DOI: https://doi.org/10.1103/PhysRevLett.119.090603

M. Campisi and R. Fazio, “The power of a critical heat engine,” Nat. Commun., vol. 7, no. 1, p. 11895, 2016. https://doi.org/10.1038/ncomms11895 DOI: https://doi.org/10.1038/ncomms11895

R. Shankar, “Principles of quantum mechanics”. New York: Plenum Press. 1994. https://doi.org/10.1007/978-1-4757-0576-8 DOI: https://doi.org/10.1007/978-1-4757-0576-8

Illustration of a four-step quantum Carnot cycle, where S denote the length of the different types of potential wells and F is the force exerted on the wall of the wells



How to Cite

Herrera Alcantar, H. K., Carvajal García, J. C., Rosales Pérez, O., Villarreal-Sánchez, R. C., & Iglesias-Vázquez, P. E. (2019). Dimensionality and geometry effects on a quantum carnot engine efficiency. REVISTA DE CIENCIAS TECNOLÓGICAS, 2(1), 45–48. https://doi.org/10.37636/recit.v214548



Case studies