Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Some implications of three generalized uncertainty principles in statistical mechanics of an ideal gas

  • 32 Accesses

  • 1 Citations

Abstract

Several approaches to quantum gravity and high-energy physics predict the existence of a minimum length scale due to quantum gravitational corrections leading to the deformation/generalization of the uncertainty principle (GUP). Various mathematical forms of GUP were introduced in the literature and their implications in different fields ranging from nanoscale to large scale were discussed in the literature. In this paper, we study three dissimilar forms of GUP and we discuss their implications in statistical mechanics of an ideal gas. A number of features were obtained, discussed, and analyzed accordingly.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    A. Kempf, G. Mangano, R.B. Mann, Hilbert space representation of the minimal length uncertainty relation. Phys. Rev. D 52, 1108 (1995)

  2. 2.

    K. Nozari, P. Pedram, Minimal length and bouncing particle spectrum. Europhys. Lett. 92, 50013 (2010)

  3. 3.

    L. Perivolaropoulos, Cosmological horizons uncertainty principle and maximum length quantum mechanics. Phys. Rev. D 95, 103523 (2017)

  4. 4.

    M. Maggiore, Quantum groups, gravity and the generalized uncertainty principle. Phys. Rev. D 49, 5182–5187 (1994)

  5. 5.

    L.N. Chang, Z. Lewis, D. Minic, T. Takeuchi, On the minimal length uncertainty relation and the foundations of string theory. Adv. High Energy Phys. 2011, Article ID 493514 (2011)

  6. 6.

    L.J. Garay, Quantum gravity and minimum length. Int. J. Mod. Phys. A 10, 145 (1995)

  7. 7.

    S. Hossenfelder, M. Bleicher, S. Hofmann, J. Ruppert, S. Scherer, H. Stöcker, Signatures in the Planck regime. Phys. Lett. B 575, 85–99 (2003)

  8. 8.

    C. Bambi, F.R. Urban, Natural extension of the generalized uncertainty principle. Class. Quantum Gravity 25, Article ID 095006 (2008)

  9. 9.

    K. Nozari, A. Etemadi, Minimal length maximal momentum and Hilbert space representation of quantum mechanics. Phys. Rev. D 85, 104029 (2012)

  10. 10.

    P. Pedram, A higher order GUP with minimal length uncertainty and maximal momentum. Phys. Lett. B 714, 638–645 (2012)

  11. 11.

    S. Das, E.C. Vagenas, Phenomenological implications of the generalized uncertainty principle. Can. J. Phys. 87, 233–240 (2009)

  12. 12.

    S. Das, E.C. Vagenas, Universality of quantum gravity corrections. Phys. Rev. Lett. 101, 2213 (2008)

  13. 13.

    C. Conti, Quantum gravity simulation by nonparaxial nonlinear optics. Phys. Rev. A 89, 061801 (2014)

  14. 14.

    M.C. Braidotti, Z.H. Musslimani, Conti, Generalized uncertainty principle and analogue of quantum gravity in optics. Phys. D 338, 34–41 (2017)

  15. 15.

    A.F. Ali, M. Moussa, Towards thermodynamics with generalized uncertainty relation. Adv. High Energy Phys. 2014, Article ID 629148 (2014)

  16. 16.

    M. Sprenger, M. Bleicher, P. Nicolini, Neutrino oscillations as a novel probe for a minimal length. Class. Quantum Gravity 28, 235019 (2011)

  17. 17.

    K. Nozari, S. Saghafi, Natural cutoffs and quantum tunneling from black hole horizon. JHEP 11, 005 (2012)

  18. 18.

    K. Nozari, S.H. Mehdipour, Implications of minimal length scale on the statistical mechanics of ideal gas. Chaos Solitons Fractals 32, 1637–1644 (2007)

  19. 19.

    S. Bensalem, D. Bouaziz, Statistical description of an ideal gas in maximal length quantum mechanics. Phys. A 523, 583–592 (2019)

  20. 20.

    R.A. El-Nabulsi, Nonlocal uncertainty and its implications in quantum mechanics at ultramicroscopic scales. Quant. Stud. Math. Found. 6, 123–133 (2019)

  21. 21.

    M. Tomamichel, E. Hanggi, The link between entropic uncertainty and nonlocality. J. Phys. A Math. Gen. 46, 055301 (2013)

  22. 22.

    W.S. Chung, H. Hassanabadi, A new higher order GUP: one dimensional quantum system. Eur. Phys. J. C 79, 213 (2019)

  23. 23.

    H. Hassanabadi, E. Maghsoodi, W.S. Chung, Analysis of black hole thermodynamics with a new higher order generalized uncertainty principle. Eur. Phys. J. C 79, 358 (2019)

  24. 24.

    S. Kouwn, Implications of minimum and maximum length scales in cosmology. Phys. Dark Univ. 21, 76–81 (2018)

  25. 25.

    M. Bojowald, A. Kempf, Generalized uncertainty principles and localization in discrete space. Phys. Rev. D 86, 085017 (2012)

  26. 26.

    A.F. Ali, M.M. Khalil, E.C. Vagenas, Minimal length in quantum gravity and gravitational measurements. Eur. Phys. Lett. 112, 20005 (2015)

  27. 27.

    K. Nouicer, Quantum-corrected black hole thermodynamics to all orders in the Planck length. Phys. Lett. B 646, 64–71 (2007)

  28. 28.

    Y.-G. Miao, Y.-J. Zhao, Interpretation of the cosmological constant problem within the framework of generalized uncertainty principle. Int. J. Mod. Phys. D 23, 1450062 (2014)

  29. 29.

    H. Shababi, W.S. Chung, On the two new types of the higher order GUP with minimal length uncertainty and maximal momentum. Phys. Lett. B 770, 445–450 (2017)

  30. 30.

    H. Shababi, Statistical mechanics of ideal gas in the presence of minimal length and maximal momentum. J. Theor. Phys. 1, 236 (2012)

  31. 31.

    M. Abbasiyan-Motlaq, P. Pedram, The minimal length and the quantum partition function. J. Stat. Mech. 2014, Article ID P08002 (2014)

  32. 32.

    A. Alizadeh, J. Nozari, Some details of statistical mechanics of many-body systems in the presence of a measurable minimal length. Acta Phys. Polon. A 132, 1329–1332 (2017)

  33. 33.

    S. Bensalem, D. Bouaziz, Statistical description of an ideal gas in maximum length quantum mechanics. Phys. A Stat. Mech. Appl. 523, 583–592 (2019)

  34. 34.

    T.F. Fiyto, Statistical physics in deformed spaces with minimal length. Phys. Lett. A 37, 5872–5877 (2008)

  35. 35.

    R.K. Pathria, Statistical Mechanics (Butterworth-Heinemann, Oxford, 1996)

Download references

Acknowledgements

The author would like to thank the anonymous referees for their useful comments and valuable suggestions.

Author information

Correspondence to Rami Ahmad El-Nabulsi.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

El-Nabulsi, R.A. Some implications of three generalized uncertainty principles in statistical mechanics of an ideal gas. Eur. Phys. J. Plus 135, 34 (2020). https://doi.org/10.1140/epjp/s13360-019-00051-w

Download citation