Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Breuer, H.-P., Petruccione, F.: The theory of open quantum systems. Oxford University Press, Oxford (2007).
Alicki, R., Lendi, K.: Quantum Dynamical Semigroups and Applications. Springer, Berlin (2007).
Rivas, Á., Huelga, S.F.: Open Quantum Systems, an Introduction. Springer, Heidelberg (2012).
Vasile, R., Olivares, S., Paris, M.G.A., Maniscalco, S.: Phys. Rev. A. 83, 042321 (2011).
Huelga, S.F., Rivas, A., Plenio, M.B.: Phys. Rev. Lett. 108, 160402 (2012).
Chin, A.W., Huelga, S.F., Plenio, M.B.: ibid. 109, 233601 (2012).
Laine, E.-M., Breuer, H.-P., Piilo, J.: Sci. Rep. 4, 4620 (2014).
Addis, C., Bylicka, B., ChruÅżciÅĎski, D., Maniscalco, S.: Phys. Rev. A. 90, 052103 (2014).
Felipe, Fanchini, F., Karpat, G., Castelano, L.K., Rossatto, D.Z.: phys. Rev. A. 88, 012105 (2013).
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.
Bylicka, B., Tukiainen, M., Piilo, J., Chruscinski, D., Maniscalco, S.: arXiv:hep-th/1504.06533.
Karpat, G., Piilo, J., Maniscalco, S.: Europhys. Lett. 111, 5 (2015).
Piilo, J., Maniscalco, S., Harkonen, K., Suominen, K.-A.: Phys. Rev. Lett. 100, 180402 (2008).
Rivas, Á., Huelga, S.F., Plenio, M.B.: Phys. Rev. Lett. 105, 050403 (2010).
Hou, S.C., Yi, X.X., Yu, S.X., Oh, C.H.: Phys. Rev. A. 86, 012101 (2012).
Breuer, H.-P., Laine, E.-M., Piilo, J.: Phys. Rev. Lett. 103, 210401 (2009).
Luo, S., Fu, S., Song, H.: Phys. Rev. A. 86, 044101 (2012).
Rajagopal, A.K., Usha Devi, A.R., Rendell, R.W.: Phys. Rev. A. 82, 042107 (2010).
lu, X.-M., Wang, X., Sun, C.P.: Phys. Rev. A. 82, 042103 (2010).
Lorenzo, S., Plastina, F., Paternostro, M.: Phys. Rev. A. 88 (R), 020102 (2013).
licka, B., Chruściński, D., Maniscalco, S.: Sci. Rep. 4 (2014), 5720.
Alipour, S., Mani, A., Rezakhani, A.T.: Phys. Rev. A. 85, 052108 (2012).
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).
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).
Schumacher, B.W.: Phys. Rev. A. 54, 2614 (1996).
Sagawa, T., Ueda, M.: New J. Phys. 5, 125012 (2013).
Vedral, V.: J. Phys. Conf. Ser. 143, 012010 (2009).
Jamiolkowski, A.: Rep. Math. Phys. 3, 275 (1972).
Choi, M.-D.: Lin. Alg. Appl. 10, 285 (1975).
Pati, A.: arXiv:hep-th/1208.4804.
Palma, G.M., Suominen, K.-A., Ekert, A.K.: Proc. Roy. Soc. Lond. A. 452, 567 (1996).
Leggett, J.A.: Rev. Mod. Phys. 59, 1 (1987).
Liu, J., Lu, X.-M., Wang, X.: Phys. Rev. A. 87, 042103 (2013).
Garraway, B.M.: Rev, Phys. A. 55 (3), 2290 (1997).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Salimi, S., Haseli, S., Khorashad, A.S. et al. The Role of the Total Entropy Production in the Dynamics of Open Quantum Systems in Detection of Non-Markovianity. Int J Theor Phys 55, 4089–4099 (2016). https://doi.org/10.1007/s10773-016-3037-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-016-3037-4