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  • Letter
  • Open Access

Decoherence limit of quantum systems obeying generalized uncertainty principle: New paradigm for Tsallis thermostatistics

Petr Jizba*

Gaetano Lambiase† and Giuseppe Gaetano Luciano‡

Luciano Petruzziello§

  • FNSPE, Czech Technical University in Prague, Břehová 7, 115 19, Prague, Czech Republic and ITP, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany

  • Dipartimento di Fisica, Università di Salerno, Via Giovanni Paolo II, 132 I-84084 Fisciano (SA), Italy and INFN, Sezione di Napoli, Gruppo collegato di Salerno, Italy

  • Dipartimento di Fisica, Università di Salerno, Via Giovanni Paolo II, 132 I-84084 Fisciano (SA), Italy; INFN, Sezione di Napoli, Gruppo collegato di Salerno, Italy; and Dipartimento di Ingegneria, Università di Salerno, Via Giovanni Paolo II, 132 I-84084 Fisciano (SA), Italy

  • *p.jizba@fjfi.cvut.cz
  • †lambiase@sa.infn.it
  • ‡gluciano@sa.infn.it
  • §lupetruzziello@unisa.it
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Phys. Rev. D 105, L121501 – Published 15 June, 2022

DOI: https://doi.org/10.1103/PhysRevD.105.L121501

Abstract

The generalized uncertainty principle (GUP) is a phenomenological model whose purpose is to account for a minimal length scale (e.g., Planck scale or characteristic inverse-mass scale in effective quantum description) in quantum systems. In this paper, we study possible observational effects of GUP systems in their decoherence domain. We first derive coherent states associated to GUP and unveil that in the momentum representation they coincide with Tsallis probability amplitudes, whose nonextensivity parameter q monotonically increases with the GUP deformation parameter β. Second, for β<0 (i.e., q<1), we show that, due to Bekner-Babenko inequality, the GUP is fully equivalent to information-theoretic uncertainty relations based on Tsallis-entropy-power. Finally, we invoke the maximal entropy principle known from estimation theory to reveal connection between the quasiclassical (decoherence) limit of GUP-related quantum theory and nonextensive thermostatistics of Tsallis. This might provide an exciting paradigm in a range of fields from quantum theory to analog gravity. For instance, in some quantum gravity theories, such as conformal gravity, aforementioned quasiclassical regime has relevant observational consequences. We discuss some of the implications.

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Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: New route to nonextensive thermostatistics

Petr Jizba, Gaetano Lambiase, Giuseppe Gaetano Luciano, and Luciano Petruzziello
Phys. Rev. D 108, 064024 (2023)

Article Text

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References (70)

  1. D. Amati, M. Ciafaloni, and G. Veneziano, Phys. Lett. B 197, 81 (1987).
  2. D. Amati, M. Ciafaloni, and G. Veneziano, Phys. Lett. B 216, 41 (1989).
  3. W. S. Chung and H. Hassanabadi, Phys. Lett. B 785, 127 (2018).
  4. C. Rovelli, J. Phys. Conf. Ser. 314, 012006 (2011).
  5. A. Ashtekar, A. Corichi, and J. A. Zapata, Classical Quantum Gravity 15, 2955 (1998).
  6. J. Magueijo and L. Smolin, Phys. Rev. Lett. 88, 190403 (2002).
  7. J. Magueijo and L. Smolin, Phys. Rev. D 67, 044017 (2003).
  8. M. Maggiore, Phys. Lett. B 304, 65 (1993).
  9. R. C. S. Bernardo and J. P. H. Esguerra, Ann. Phys. (Amsterdam) 391, 293 (2018).
  10. A. M. Frassino and O. Panella, Phys. Rev. D 85, 045030 (2012).
  11. M. Blasone, G. Lambiase, G. G. Luciano, L. Petruzziello, and F. Scardigli, Int. J. Mod. Phys. D 29, 2050011 (2020).
  12. D. Das and E. C. Vagenas, Phys. Rev. Lett. 101, 221301 (2008).
  13. V. Husain, D. Kothawala, and S. S. Seahra, Phys. Rev. D 87, 025014 (2013).
  14. F. Scardigli, M. Blasone, G. Luciano, and R. Casadio, Eur. Phys. J. C 78, 728 (2018).
  15. P. Jizba and F. Scardigli, Phys. Rev. D 86, 025029 (2012).
  16. M. C. Braidotti, Z. H. Musslimani, and C. Conti, Physica (Amsterdam) 338D, 34 (2017).
  17. A. Tawfik and A. Diab, Int. J. Mod. Phys. D 23, 1430025 (2014).
  18. P. Jizba, H. Kleinert, and F. Scardigli, Phys. Rev. D 81, 084030 (2010).
  19. E. Schrödinger, Collected Papers on Wave Mechanics (Blackie, London, 1928), p. 41.
  20. H. P. Robertson, Phys. Rev. 34, 163 (1929).
  21. N. Mukhopadhyay, Probability and Statistical Inference (Marcel Dekker, New York, 2000).
  22. R. J. Adler and D. I. Santiago, Mod. Phys. Lett. A 14, 1371 (1999).
  23. C. Kiefer, Quantum Gravity (Oxford Science Publications, Oxford, 2012).
  24. C. Kiefer, The semiclassical approximation to quantum gravity, in Canonical Gravity: From Classical to Quantum, edited by J. Ehlers and H. Friedrich, Lecture Notes in Physics (Springer, Berlin, 1994), Vol. 434.
  25. W. H. Zurek, S. Habib, and J. P. Paz, Phys. Rev. Lett. 70, 1187 (1993).
  26. S. M. Dutra, J. Mod. Opt. 45, 759 (1998).
  27. A. L. Matacz, Phys. Rev. D 49, 788 (1994).
  28. M. M. Nieto and L. M. Simmons, Jr., Phys. Rev. Lett. 41, 207 (1978).
  29. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevD.105.L121501 for detailed technical exposition of Tsallis-type coherent states and associated entropy powers.
  30. E. T. Jaynes, Phys. Rev. 106, 620 (1957).
  31. E. T. Jaynes, Phys. Rev. 108, 171 (1957).
  32. See e.g., Entropy Measures, Maximum Entropy Principle and Emerging Applications, edited by Karmeshu (Springer-Verlag, Berlin, 2003).
  33. See e.g., C. Tsallis, Introduction to Nonextensive Statistical Mechanics; Approaching a Complex World (Springer, New York, 2009).
  34. S. Abe, S. Martínez, F. Pennini, and A. Plastino, Phys. Lett. A 281, 126 (2001).
  35. S. Abe, Physica (Amsterdam) 300A, 417 (2001).
  36. A. Kempf, G. Mangano, and R. B. Mann, Phys. Rev. D 52, 1108 (1995).
  37. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980).
  38. L. Buoninfante, G. G. Luciano, and L. Petruzziello, Eur. Phys. J. C 79, 663 (2019).
  39. Y. C. Ong, J. Cosmol. Astropart. Phys. 09 (2018) 015.
  40. W. Thistleton, J. A. Marsh, K. Nelson, and C. Tsallis, IEEE Trans. Inf. Theory 53, 4805 (2007).
  41. C. Tsallis, J. Stat. Phys. 52, 479 (1988).
  42. P. Jizba, J. Korbel, and V. Zatloukal, Phys. Rev. E 95, 022103 (2017).
  43. P. Jizba and J. Korbel, Phys. Rev. Lett. 122, 120601 (2019).
  44. P. Jizba, Y. Ma, A. Hayes, and J. A. Dunningham, Phys. Rev. E 93, 060104(R) (2016).
  45. J. P. Paz and W. H. Zurek, Phys. Rev. Lett. 82, 5181 (1999).
  46. A. Venugopalan, Phys. Rev. A 61, 012102 (1999).
  47. D. A. R. Dalvit, J. Dziarmaga, and W. H. Zurek, Phys. Rev. A 72, 062101 (2005).
  48. J. P. Paz and W. H. Zurek, in Coherent Atomic Matter Waves. Les Houches—Ecole d’Ete de Physique Theorique, edited by R. Kaiser, C. Westbrook, and F. David (Springer, Berlin, 2001), Vol. 72.
  49. E. P. Verlinde, J. High Energy Phys. 04 (2011) 029.
  50. C. Tsallis and L. J. L. Cirto, Eur. Phys. J. C 73, 2487 (2013); C. Tsallis, Entropy 22, 17 (2019).
  51. T. L. Hill, Thermodynamics of Small Systems (Dover, New York, 1994).
  52. J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973).

  53. Note that λC is the minimal distance at which a particle still retains its single-particle picture.

  54. S. Curilef, A. R. Plastino, R. S. Wedemann, and A. Daffertshofer, Phys. Lett. A 372, 2341 (2008).
  55. S. Curilef, A. R. Plastino, R. S. Wedemann, and A. Daffertshofer, Phys. Lett. B 767, 242 (2017).
  56. P. D. Mannheim and J. G. O’Brien, Phys. Rev. Lett. 106, 121101 (2011).
  57. P. D. Mannheim and J. G. O’Brien, Phys. Rev. D 85, 124020 (2012).
  58. J. G. O’Brien and P. D. Mannheim, Mon. Not. R. Astron. Soc. 421, 1273 (2012).
  59. J. G. O’Brien, T. L. Chiarelli, and P. D. Mannheim, Phys. Lett. B 782, 433 (2018).
  60. J. Sultana, D. Kazanas, and J. L. Said, Phys. Rev. D 86, 084008 (2012).
  61. D. Grumiller, Phys. Rev. Lett. 105, 211303 (2010).
  62. S. Carloni, D. Grumiller, and F. Preis, Phys. Rev. D 83, 124024 (2011).
  63. S. H. Mazharimousavi and M. Halilsoy, Mod. Phys. Lett. A 28, 1350073 (2013).
  64. C. Kiefer, I. Lohmar, D. Polarski, and A. A. Starobinsky, Classical Quantum Gravity 24, 1699 (2007).
  65. C. P. Burgess, R. Holman, and D. Hoover, Phys. Rev. D 77, 063534 (2008).
  66. S. Abe, Phys. Lett. A 263, 424 (1999); 267, 456(E) (2000).
  67. J. Du, Physica (Amsterdam) 335A, 107 (2004).
  68. J. D. Barrow and A. Paliathanasis, Phys. Rev. D 94, 083518 (2016).
  69. J. D. Barrow and A. Paliathanasis, Gen. Relativ. Gravit. 50, 82 (2018).
  70. A. Vilenkin and L. H. Ford, Phys. Rev. D 26, 1231 (1982).

Outline

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Phys. Rev. D 105, L121501– Published 15 June, 2022
  • Received 12 December 2021
  • Revised 20 January 2022
  • Accepted 30 May 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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