Abstract
We study the reversible quantum Stirling cycle with a single spin or two coupled spins as the working substance. With the single spin as the working substance, we find that under certain conditions the reversed cycle of a heat engine is NOT a refrigerator, this feature holds true for a Stirling heat engine with an ion trapped in a shallow potential as its working substance. The efficiency of quantum Stirling heat engine can be higher than the efficiency of the Carnot engine, but the performance coefficient of the quantum Stirling refrigerator is always lower than its classical counterpart. With two coupled spins as the working substance, we find that a heat engine can turn to a refrigerator due to the increasing of the coupling constant, this can be explained by the properties of the isothermal line in the magnetic field-entropy plane.
Similar content being viewed by others
References
M. Born, V. Fork, Z. Phys. 51, 165 (1928)
A. Messiah, Quantum Mechanics (Dover, New York, 1999)
T.D. Kieu, Phys. Rev. Lett. 93, 140403 (2004)
T.D. Kieu, Eur. Phys. J. D 39, 115 (2006)
H.T. Quan, Y.X. Liu, C.P. Sun, F. Nori, Phys. Rev. E 76, 031105 (2007)
H.T. Quan, Phys. Rev. E 79, 041129 (2009)
P. Perrot, A to Z of Thermodynamics (Oxford University Press, Oxford, 1998)
T. Feldmann, R. Kosloff, Phys. Rev. E 61, 4774 (2000)
T. Feldmann, R. Kosloff, Phys. Rev. E 68, 016101 (2003)
T. Feldmann, R. Kosloff, Phys. Rev. E 70, 046110 (2004)
J.Z. He, J.C. Chen, B. Hua, Phys. Rev. E 65, 036145 (2002)
C.M. Bender, D.C. Body, B.K. Meister, J. Phys. A 33, 4427 (2000)
J.H. Wang, J.Z. He, X. He, Phys. Rev. E 84, 041127 (2011)
J.H. Wang, Z.Q. Wu, J.Z. He, Phys. Rev. E 85, 041148 (2012)
H.T. Quan, P. Zhang, C.P. Sun, Phys. Rev. E 72, 056110 (2005)
H. Li, J. Zou, W.L. Yu, L. Li, B.M. Xu, B. Shao, Eur. Phys. J. D 67, 134 (2013)
B.H. Lin, J.C. Chen, Phys. Rev. E 67, 046105 (2003)
T. Zhang, W.T. Liu, P.X. Chen, C.Z. Li, Phys. Rev. A 75, 062102 (2007)
G. Thomas, R.S. Johal, Phys. Rev. E 83, 031135 (2011)
X.L. Huang, L.C. Wang, X.X. Yi, Phys. Rev. E 87, 012144 (2013)
E. Muñoz, F.J. Peña, Phys. Rev. E 86, 061108 (2012)
M. Esposito, R. Kawai, C. Van den Broeck, Phys. Rev. E 81, 041106 (2010)
J. Hoppenau, M. Niemann, A. Engel, Phys. Rev. E 87, 062127 (2013)
T. Feldmann, R. Kosloff, Phys. Rev. E 85, 051114 (2012)
H. Wang, Phys. Scr. 87, 055009 (2013)
C. Van den Broeck, N. Kumar, K. Lindenberg, Phys. Rev. E 708, 210602 (2012)
G. Thomas, R.S. Johal, Phys. Rev. E 85, 041146 (2012)
H. Yan, H. Guo, Phys. Rev. E 86, 051135 (2012)
M.J. Henrich, G. Mahler, M. Michel, Phys. Rev. E 75, 051118 (2007)
F. Tonner, G. Mahler, Phys. Rev. E 72, 066118 (2005)
O. Abah, J. Robnagel, G. Jacob, S. Deffner, F. Schmide-Kaler, K. Singer, E. Lutz, Phys. Rev. Lett. 109, 203006 (2012)
O. Fialko, D.W. Hallwood, Phys. Rev. Lett. 108, 085303 (2012)
M.O. Scully, K.R. Chapin, K.E. Dorfman, M.B. Kim, A. Svidzinsky, Proc. Natl. Sci. 108, 15097 (2011)
S. Rahav, U. Harbola, S. Mukamel, Phys. Rev. A 86, 043843 (2012)
L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)
M.O. Scully, M.S. Zubairy, G.S. Agarwal, H. Walther, Science 299, 862 (2003)
M.O. Scully, in Quantum Limits to the Second Law: First International Conference, edited by D.P. Sheehan (AIP Press, Melville, 2002), pp. 83–91
Yu.V. Rostovtsev, Z.E. Sariyianni, M.O. Scully, Laser Phys. 13, 375 (2003)
X.L. Huang, T. Wang, X.X. Yi, Phys. Rev. E 86, 051105 (2012)
M.O. Scully, Phys. Rev. Lett. 87, 220601 (2001)
M.O. Scully, Phys. Rev. Lett. 88, 050602 (2002)
H.T. Quan, Y.D. Wang, Y.X. Liu, C.P. Sun, F. Nori, Phys. Rev. Lett. 97, 180402 (2006)
A. Levy, R. Kosloff, Phys. Rev. Lett. 108, 070604 (2012)
D. Mandal, H.T. Quan, C. Jarzynski, Phys. Rev. Lett. 111, 030602 (2013)
S. Abe, S. Okuyama, Phys. Rev. E 83, 021121 (2011)
S. Abe, S. Okuyama, Phys. Rev. E 85, 011104 (2012)
A. Levy, R. Alicki, R. Kosloff, Phys. Rev. E 85, 061126 (2012).
S. Hormoz, Phys. Rev. E 87, 022129 (2013)
S.W. Kim, T. Sagawa, S.E. Liberato, M. Ueda, Phys. Rev. Lett. 106, 070401 (2011)
C.Y. Cai, H. Dong, C.P. Sun, Phys. Rev. E 85, 031114 (2012)
Y. Lu, G.L. Long, Phys. Rev. E 85, 011125 (2012)
H. Li, J. Zou, J.G. Li, B. Shao, L.A. Wu, Ann. Phys. 327, 2955 (2012)
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Huang, XL., Niu, XY., Xiu, XM. et al. Quantum Stirling heat engine and refrigerator with single and coupled spin systems. Eur. Phys. J. D 68, 32 (2014). https://doi.org/10.1140/epjd/e2013-40536-0
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjd/e2013-40536-0