International Journal of Theoretical Physics

, Volume 55, Issue 9, pp 4089–4099 | Cite as

The Role of the Total Entropy Production in the Dynamics of Open Quantum Systems in Detection of Non-Markovianity



The interaction between system and environment is a fundamental concept in the theory of open quantum systems. As a result of the interaction, an amount of correlation (both classical and quantum) emerges between the system and the environment. In this work, we recall the quantity that will be very useful to describe the emergence of the correlation between the system and the environment, namely, the total entropy production. Appearance of total entropy production is due to the entanglement production between the system and the environment. In this work, we discuss about the role of the total entropy production for detecting the non-Markovianity. By utilizing the relation between the total entropy production and total correlation between subsystems, one can see a temporary decrease of total entropy production is a signature of non-Markovianity. We apply our criterion for the special case, where the composite system has initial correlation with environment.


Total entropy production Open quantum systems Non-Markovianity 


  1. Breuer, H.-P., Petruccione, F.: The theory of open quantum systems. Oxford University Press, Oxford (2007).CrossRefMATHGoogle Scholar
  2. Alicki, R., Lendi, K.: Quantum Dynamical Semigroups and Applications. Springer, Berlin (2007).MATHGoogle Scholar
  3. Rivas, Á., Huelga, S.F.: Open Quantum Systems, an Introduction. Springer, Heidelberg (2012).CrossRefMATHGoogle Scholar
  4. Vasile, R., Olivares, S., Paris, M.G.A., Maniscalco, S.: Phys. Rev. A. 83, 042321 (2011).ADSCrossRefGoogle Scholar
  5. Huelga, S.F., Rivas, A., Plenio, M.B.: Phys. Rev. Lett. 108, 160402 (2012).ADSCrossRefGoogle Scholar
  6. Chin, A.W., Huelga, S.F., Plenio, M.B.: ibid. 109, 233601 (2012).ADSCrossRefGoogle Scholar
  7. Laine, E.-M., Breuer, H.-P., Piilo, J.: Sci. Rep. 4, 4620 (2014).ADSCrossRefGoogle Scholar
  8. Addis, C., Bylicka, B., ChruÅżciÅĎski, D., Maniscalco, S.: Phys. Rev. A. 90, 052103 (2014).ADSCrossRefGoogle Scholar
  9. Felipe, Fanchini, F., Karpat, G., Castelano, L.K., Rossatto, D.Z.: phys. Rev. A. 88, 012105 (2013).ADSCrossRefGoogle Scholar
  10. Liu, B.-H., Hu, X.-M., Huang, Y.-F., Li, C.-F., Guo, G.-C., Karlsson, A., Laine, E.-M., Maniscalco, S., Macchiavello, C., Piilo, J.: arXiv:hep-th/1504.07572.
  11. Bylicka, B., Tukiainen, M., Piilo, J., Chruscinski, D., Maniscalco, S.: arXiv:hep-th/1504.06533.
  12. Karpat, G., Piilo, J., Maniscalco, S.: Europhys. Lett. 111, 5 (2015).CrossRefGoogle Scholar
  13. Piilo, J., Maniscalco, S., Harkonen, K., Suominen, K.-A.: Phys. Rev. Lett. 100, 180402 (2008).ADSMathSciNetCrossRefGoogle Scholar
  14. Rivas, Á., Huelga, S.F., Plenio, M.B.: Phys. Rev. Lett. 105, 050403 (2010).ADSMathSciNetCrossRefGoogle Scholar
  15. Hou, S.C., Yi, X.X., Yu, S.X., Oh, C.H.: Phys. Rev. A. 86, 012101 (2012).ADSCrossRefGoogle Scholar
  16. Breuer, H.-P., Laine, E.-M., Piilo, J.: Phys. Rev. Lett. 103, 210401 (2009).ADSMathSciNetCrossRefGoogle Scholar
  17. Luo, S., Fu, S., Song, H.: Phys. Rev. A. 86, 044101 (2012).ADSCrossRefGoogle Scholar
  18. Rajagopal, A.K., Usha Devi, A.R., Rendell, R.W.: Phys. Rev. A. 82, 042107 (2010).ADSCrossRefGoogle Scholar
  19. lu, X.-M., Wang, X., Sun, C.P.: Phys. Rev. A. 82, 042103 (2010).ADSCrossRefGoogle Scholar
  20. Lorenzo, S., Plastina, F., Paternostro, M.: Phys. Rev. A. 88 (R), 020102 (2013).ADSCrossRefGoogle Scholar
  21. licka, B., Chruściński, D., Maniscalco, S.: Sci. Rep. 4 (2014), 5720.Google Scholar
  22. Alipour, S., Mani, A., Rezakhani, A.T.: Phys. Rev. A. 85, 052108 (2012).ADSCrossRefGoogle Scholar
  23. Fanchini, F.F., Karpat, G., Çakmak, B., Castelano, L.K., Aguilar, G.H., Farías, O.J., Walborn, S.P., Souto Riberio, P.H., de Oliveira, M.C.: Phys. Rev. Lett. 112, 210402 (2014).ADSCrossRefGoogle Scholar
  24. Haseli, S., Karpat, G., Salimi, S., Khorashad, A.S., Fanchini, F.F., akmak, B., Aguilar, G.H., Walborn, S.P., Souto Ribeiro, P.H.: Phys. Rev. A. 90, 052118 (2014).ADSCrossRefGoogle Scholar
  25. Schumacher, B.W.: Phys. Rev. A. 54, 2614 (1996).ADSCrossRefGoogle Scholar
  26. Sagawa, T., Ueda, M.: New J. Phys. 5, 125012 (2013).MathSciNetCrossRefGoogle Scholar
  27. Vedral, V.: J. Phys. Conf. Ser. 143, 012010 (2009).ADSCrossRefGoogle Scholar
  28. Jamiolkowski, A.: Rep. Math. Phys. 3, 275 (1972).ADSMathSciNetCrossRefGoogle Scholar
  29. Choi, M.-D.: Lin. Alg. Appl. 10, 285 (1975).CrossRefGoogle Scholar
  30. Pati, A.: arXiv:hep-th/1208.4804.
  31. Palma, G.M., Suominen, K.-A., Ekert, A.K.: Proc. Roy. Soc. Lond. A. 452, 567 (1996).ADSMathSciNetCrossRefGoogle Scholar
  32. Leggett, J.A.: Rev. Mod. Phys. 59, 1 (1987).ADSCrossRefGoogle Scholar
  33. Liu, J., Lu, X.-M., Wang, X.: Phys. Rev. A. 87, 042103 (2013).ADSCrossRefGoogle Scholar
  34. Garraway, B.M.: Rev, Phys. A. 55 (3), 2290 (1997).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • S. Salimi
    • 1
  • S. Haseli
    • 1
  • A. S. Khorashad
    • 1
  • F. Adabi
    • 1
  1. 1.Department of PhysicsUniversity of KurdistanSanandajIran

Personalised recommendations