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de Bruijn-type identity for systems with flux

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Abstract

We show that an information-theoretic relation called the de Bruijn-type identity can be reformulated in a physical context with probability currents. The time derivatives of relative entropies under the continuity equation are presented, which shows that the conservation of distance between a pair of distributions is generally not guaranteed. As an important implication of these results, we discuss and present a possible conceptual framework for the classical no-cloning (deleting) theorem and qualitatively assert that we can attribute the perfect performance of the operating machine to the openness (non-vanishing flow at boundaries between the processing machine and the system) during the process.

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References

  1. A.J. Stam, Inf. Contr. 2, 101 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  2. T. Cover, J. Thomas, Elements of Information Theory, 2nd edn. (Wiley-Interscience, New York, 2006)

  3. A. Dembo, T. Cover, J. Thomas, IEEE Trans. Inf. Theory 37, 1501 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  4. K.R. Narayanan, A.R. Srinivasa, arXiv/0711.1460v2

  5. D. Guo, Proc. IEEE Int. Symp. Inf. Theory 3, 814 (2009)

    Google Scholar 

  6. S. Kullback, R.A. Leibler, Ann. Math. Stat. 22, 79 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  7. S. Kullback, Information Theory and Statistics (Wiley, New York, 1959)

  8. G. Blower, Random Matrices: High Dimensional Phenomena, ser. London Mathematical Society Lecture Notes (Cambridge University Press, Cambridge, 2009), Chap. 6, p. 211

  9. C. Villani, Topics in Optimal Transportation, Graduate Studies in Mathematics (American Mathematical Society, 2000), Vol. 58, p. 278

  10. S. Verdú, IEEE Trans. Inf. Theor. 56, 3712 (2010)

    Article  Google Scholar 

  11. M. Hirata, A. Nemoto, H. Yoshida, Entropy 14, 1469 (2012)

    Article  MathSciNet  Google Scholar 

  12. M.C. Mackey, Rev. Mod. Phys. 61, 981 (1989)

    Article  ADS  Google Scholar 

  13. A. Daffertshofer, A.R. Plastino, A. Plastino, Phys. Rev. Lett. 88, 210601 (2002)

    Article  ADS  Google Scholar 

  14. A.R. Plastino, A. Daffertshofer, Phys. Rev. Lett. 93, 138701 (2004)

    Article  ADS  Google Scholar 

  15. T.A. Walker, S. Braunstein, Phys. Rev. Lett. 98, 080501 (2007)

    Article  ADS  Google Scholar 

  16. T. Yamano, O. Iguchi, Europhys. Lett. 83, 50007 (2008)

    Article  ADS  Google Scholar 

  17. J. Antolín, J.C. Angulo, S. López-Rosa, J. Chem. Phys. 130, 074110 (2009)

    Article  ADS  Google Scholar 

  18. P. Sánchez-Moreno, A. Zarzo, J.S. Dehesa, J. Phys. A 45, 125305 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  19. C. Zander, A.R. Plastino, Europhys. Lett. 86, 18004 (2009)

    Article  ADS  Google Scholar 

  20. T. Morimoto, J. Phys. Soc. Jpn 12, 328 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  21. I. Csiszár, Stud. Math. Hung. 2, 299 (1967)

    MATH  Google Scholar 

  22. H. Risken, The Fokker-Planck Equation (Springer, New York, 1989)

  23. W.K. Wootters, W.H. Zurek, Nature 299, 802 (1982)

    Article  ADS  Google Scholar 

  24. D. Dieks, Phys. Lett. A 92, 271 (1982)

    Article  ADS  Google Scholar 

  25. V. Scarani, S. Iblisdir, N. Gisin, A. Acín, Rev. Mod. Phys. 77, 1225 (2005)

    Article  ADS  MATH  Google Scholar 

  26. D. Brody, B. Meister, Phys. Lett. A 204, 93 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. P. Blasiak, Phys. Lett. A 377, 847 (2013)

    Article  MathSciNet  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics and Physics, Faculty of Science, Kanagawa University, 2946, 6-233 Tsuchiya, Hiratsuka, 259-1293, Kanagawa, Japan

    Takuya Yamano

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  1. Takuya Yamano
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Correspondence to Takuya Yamano.

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Yamano, T. de Bruijn-type identity for systems with flux. Eur. Phys. J. B 86, 363 (2013). https://doi.org/10.1140/epjb/e2013-40634-9

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  • DOI: https://doi.org/10.1140/epjb/e2013-40634-9

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