Table of Contents
Advances in Statistics
Volume 2015 (2015), Article ID 581259, 8 pages
http://dx.doi.org/10.1155/2015/581259
Research Article

Relative Entropies and Jensen Divergences in the Classical Limit

1La Plata National University and Argentina’s National Research Council (IFLP-CCT-CONICET)-C, C. 727, 1900 La Plata, Argentina
2Comision de Investigaciones Científicas (CIC), Argentina

Received 30 September 2014; Revised 21 December 2014; Accepted 11 January 2015

Academic Editor: Jos De Brabanter

Copyright © 2015 A. M. Kowalski and A. Plastino. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Kullback and R. A. Leibler, “On information and sufficiency,” Annals of Mathematical Statistics, vol. 22, pp. 79–86, 1951. View at Publisher · View at Google Scholar · View at MathSciNet
  2. P. W. Lamberti, M. T. Martin, A. Plastino, and O. A. Rosso, “Intensive entropic non-triviality measure,” Physica A—Statistical Mechanics and its Applications, vol. 334, no. 1-2, pp. 119–131, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. C. Tsallis, “Possible generalization of Boltzmann-Gibbs statistics,” Journal of Statistical Physics, vol. 52, no. 1-2, pp. 479–487, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  4. R. Hanel and S. Thurner, “Generalized Boltzmann factors and the maximum entropy principle: entropies for complex systems,” Physica A—Statistical Mechanics and its Applications, vol. 380, no. 1-2, pp. 109–114, 2007. View at Publisher · View at Google Scholar · View at Scopus
  5. G. Kaniadakis, “Statistical mechanics in the context of special relativity,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 66, no. 5, Article ID 056125, 17 pages, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. M. P. Almeida, “Generalized entropies from first principles,” Physica A: Statistical Mechanics and its Applications, vol. 300, no. 3-4, pp. 424–432, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J. Naudts, “Deformed exponentials and logarithms in generalized thermostatistics,” Physica A: Statistical Mechanics and its Applications, vol. 316, no. 1–4, pp. 323–334, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. P. A. Alemany and D. H. Zanette, “Fractal random walks from a variational formalism for Tsallis entropies,” Physical Review E, vol. 49, no. 2, pp. R956–R958, 1994. View at Publisher · View at Google Scholar · View at Scopus
  9. C. Tsallis, “Nonextensive thermostatistics and fractals,” Fractals, vol. 3, p. 541, 1995. View at Publisher · View at Google Scholar
  10. C. Tsallis, “Generalized entropy-based criterion for consistent testing,” Physical Review E, vol. 58, no. 2, pp. 1442–1445, 1998. View at Publisher · View at Google Scholar
  11. S. Tong, A. Bezerianos, J. Paul, Y. Zhu, and N. Thakor, “Nonextensive entropy measure of EEG following brain injury from cardiac arrest,” Physica A: Statistical Mechanics and Its Applications, vol. 305, no. 3-4, pp. 619–628, 2002. View at Publisher · View at Google Scholar · View at Scopus
  12. C. Tsallis, C. Anteneodo, L. Borland, and R. Osorio, “Nonextensive statistical mechanics and economics,” Physica A—Statistical Mechanics and its Applications, vol. 324, no. 1-2, pp. 89–100, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. O. A. Rosso, M. T. Martín, and A. Plastino, “Brain electrical activity analysis using wavelet-based informational tools (II): Tsallis non-extensivity and complexity measures,” Physica A, vol. 320, pp. 497–511, 2003. View at Publisher · View at Google Scholar
  14. L. Borland, “Long-range memory and nonextensivity in financial markets,” Europhysics News, vol. 36, no. 6, pp. 228–231, 2005. View at Publisher · View at Google Scholar
  15. H. Huang, H. Xie, and Z. Wang, “The analysis of VF and VT with wavelet-based Tsallis information measure,” Physics Letters A, vol. 336, no. 2-3, pp. 180–187, 2005. View at Publisher · View at Google Scholar
  16. D. G. Pérez, L. Zunino, M. T. Martín, M. Garavaglia, A. Plastino, and O. A. Rosso, “Model-free stochastic processes studied with q-wavelet-based informational tools,” Physics Letters A, vol. 364, pp. 259–266, 2007. View at Publisher · View at Google Scholar
  17. M. Kalimeri, C. Papadimitriou, G. Balasis, and K. Eftaxias, “Dynamical complexity detection in pre-seismic emissions using nonadditive Tsallis entropy,” Physica A—Statistical Mechanics and its Applications, vol. 387, no. 5-6, pp. 1161–1172, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. A. M. Kowalsi, M. T. Martin, and A. Plastino, Physica A. In press.
  19. F. Cooper, J. Dawson, S. Habib, and R. D. Ryne, “Chaos in time-dependent variational approximations to quantum dynamics,” Physical Review E—Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 57, no. 2, pp. 1489–1498, 1998. View at Google Scholar · View at Scopus
  20. A. M. Kowalski, A. Plastino, and A. N. Proto, “Classical limits,” Physics Letters. A, vol. 297, no. 3-4, pp. 162–172, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. A. M. Kowalski, M. T. Martín, A. Plastino, and O. A. Rosso, “Bandt-Pompe approach to the classical-quantum transition,” Physica D: Nonlinear Phenomena, vol. 233, no. 1, pp. 21–31, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  22. A. M. Kowalski, M. T. Martin, A. Plastino, and L. Zunino, “Tsallis' deformation parameter q quantifies the classical-quantum transition,” Physica A—Statistical Mechanics and its Applications, vol. 388, no. 10, pp. 1985–1994, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. A. M. Kowalski and A. Plastino, “Bandt-Pompe-Tsallis quantifier and quantum-classical transition,” Physica A. Statistical Mechanics and Its Applications, vol. 388, no. 19, pp. 4061–4067, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. A. Kowalski, M. T. Martin, A. Plastino, and G. Judge, “On extracting probability distribution information from time series,” Entropy, vol. 14, no. 10, pp. 1829–1841, 2012. View at Publisher · View at Google Scholar · View at Scopus
  25. H. Wold, A Study in the Analysis of Stationary Time Series, Almqvist & Wiksell, Upsala, Canada, 1938.
  26. J. Kurths and H. Herzel, “Probability theory and related fields,” Physica D, vol. 25, no. 1–3, pp. 165–172, 1987. View at Publisher · View at Google Scholar
  27. C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Physical Review Letters, vol. 88, Article ID 174102, 2002. View at Publisher · View at Google Scholar
  28. L. Borland, A. R. Plastino, and C. Tsallis, “Information gain within nonextensive thermostatistics,” Journal of Mathematical Physics, vol. 39, no. 12, pp. 6490–6501, 1998, Erratum in: Journal of Mathematical Physics, vol. 40, p. 2196, 1999. View at Publisher · View at Google Scholar
  29. A. M. Kowalski, R. D. Rossignoli, and E. M. F. Curado, Concepts and Recent Advances in Generalized Information Measures and Statistics, Bentham Science Publishers, 2013.
  30. http://en.wikipedia.org/wiki/Kullback-Leibler_divergence.
  31. J. J. Halliwell and J. M. Yearsley, “Arrival times, complex potentials, and decoherent histories,” Physical Review A, vol. 79, no. 6, Article ID 062101, 17 pages, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  32. M. J. Everitt, W. J. Munro, and T. P. Spiller, “Quantum-classical crossover of a field mode,” Physical Review A, vol. 79, no. 3, Article ID 032328, 2009. View at Publisher · View at Google Scholar
  33. H. D. Zeh, “Why Bohm's quantum theory?” Foundations of Physics Letters, vol. 12, no. 2, pp. 197–200, 1999. View at Publisher · View at Google Scholar
  34. W. H. Zurek, “Pointer basis of quantum apparatus: into what mixture does the wave packet collapse?” Physical Review D—Particles and Fields, vol. 24, no. 6, pp. 1516–1525, 1981. View at Publisher · View at Google Scholar · View at MathSciNet
  35. W. H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Reviews of Modern Physics, vol. 75, no. 3, pp. 715–775, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  36. A. M. Kowalski, M. T. Martin, A. Plastino, and A. N. Proto, “Classical limit and chaotic regime in a semi-quantum Hamiltonian,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 13, no. 8, pp. 2315–2325, 2003. View at Publisher · View at Google Scholar · View at Scopus
  37. A. Tawfik, “Impacts of generalized uncertainty principle on black hole thermodynamics and Salecker-Wigner inequalities,” Journal of Cosmology and Astroparticle Physics, vol. 2013, article 040, 2013. View at Google Scholar
  38. E. El Dahab and A. Tawfik, “Measurable maximal energy and minimal time interval,” Canadian Journal of Physics, vol. 92, no. 10, pp. 1124–1129, 2014. View at Publisher · View at Google Scholar
  39. L. L. Bonilla and F. Guinea, “Collapse of the wave packet and chaos in a model with classical and quantum degrees of freedom,” Physical Review A, vol. 45, no. 11, pp. 7718–7728, 1992. View at Publisher · View at Google Scholar
  40. A. M. Kowalski, M. T. Martín, J. Nuñez, A. Plastino, and A. N. Proto, “Quantitative indicator for semiquantum chaos,” Physical Review A, vol. 58, no. 3, pp. 2596–2599, 1998. View at Publisher · View at Google Scholar
  41. A. M. Kowalski and A. Plastino, “The Tsallis-complexity of a semiclassical time-evolution,” Physica A: Statistical Mechanics and Its Applications, vol. 391, no. 22, pp. 5375–5383, 2012. View at Publisher · View at Google Scholar · View at Scopus