Journal of Interfaces, Thin Films, and Low dimensional systems

Canonical thermostatics of ideal gas in the frame work of generalized uncertainty principle

Document Type : Original Article

Authors

1 Physics Department, Science Faculty, Islamic Azad University-North Tehran Branch, Tehran, Iran

2 Physics Department, Science Faculty, Islamic Azad University-Norht Tehran Branch, Tehran, Iran

Abstract

The statistical consequences of minimal length supposition are investigated for a canonical ensemble of ideal gas. These effects are encoded in the so-called Generalized Uncertainty Principle (GUP) of the second order. In the frame work of the considered GUP scenario, a unique partition function is obtained by using of two different methods of quantum and classical approaches. It should be noticed that here we consider the magnitude of the momentum in the deformed Hamiltonian of the model. In this way the model is different from the already existing model which does not have any significant result in quantum approach. In particular, the corrections to the thermodynamical characteristics such as the mean energy, the entropy and the density of states are achieved. The induced improvements manifest themselves at very high temperature limits. However it is shown that, if one apply the predicted observational bound on the GUP deformation parameter, the modifications become more observable even at intermediate temperatures. The deformation parameter of the considered GUP model also estimated for nowadays precision of measurements of the heat capacity of an ensemble of hydrogen atoms.

Keywords

Main Subjects

Article Title [Persian]

ترمودینامیک کانونیک مربوط به گاز کامل در چارچوب اصل عدم قطعیت تعمیم یافته

Authors [Persian]

  • صدیقه میرابوطالبی 1
  • لاله فرهنگ متین 2

1 گروه فیزیک، دانشکده علوم، دانشگاه آزاد اسلامی، واحد تهران شمال، تهران، ایران

2 گروه فیزیک ، دانشکده علوم ، دانشگاه آزاد اسلامی ، واحد شمال تهران ، تهران ، ایران

Abstract [Persian]

نتایج آماری طول کمینه در مدل کانونی آماری گاز کامل بررسی می شود.این اثر اصل عدم قطعیت تعمیم یافته مرتبه دوم نامیده می شود. در این سناریو تابع پارش از دو دیدگاه مکانیک کلاسیک و وانتوم بررسی می شود. نکته قابل توجه اینکه در محاسبات اندازه تکانه تعمیم یافته مد نظر است.
کمیات تصحیح یافته ترمودینامیکی مانند آنتروپی و تابع چگالی حالات بدست می آید.

Keywords [Persian]

  • اصل عدم قطعیت تعمیم یافته
  • طول کمینه
  • روش اختلال گاز ایده آل
  • تابع پارش کانونی
[1] G. Veneziano, “A string nature needs just two constants.” Europhysics Letters, 2 (1986) 199.
[2] D. Amati, M. Ciafaloni, G. Veneziano, “Can space-time probed below the sring size?” Physics Letters B, 216 (1989) 41.
[3] A. Kempf, G. Mangano, and R. B. Mann, “Hilbert space representation of the minimal length uncertainty relation.” Physical Review D, 52 (1995) 108.
[4] M. Maggiore, “A generalized uncertainty principle in quantum gravity.” Physics Letters B, 304 (1993) 65.
[5] P. Dzierzak, J. Jezierski, P. Malkiewicz and W. Piechocki, “The minimum length problem of loop quantum cosmology.” Acta Physica Polonica B, 41 (2010) 717.
[6] L. J. Garay, “Quantum gravity and minimal length”, International J. Modern Physics A, 10 (1995) 145.
[7] J. Magueijo and L. Smolin, Lorentz invariance with an invariant energy scale, Phys. Rev. Lett. 88 (2002) 190403.
[8] G. Amelino-Camelia, Testable scenario for relativity with minimum length, Physics Letters B, 510 (2001) 255.
[9] T. Zhu, J. R. Ren, M. F. Li, “Influence of generalized and extended uncertainty principle on thermodynamics of FRW universe.” Physics Letters B, 674 (2009) 204.
[10] A. Tawfik, H. Magdy A. Farag Ali, “Effects of quantum gravity on the inflationary parameters and thermodynamics of the early universe.” General Relativity & Gravitation, 45 (2013) 1227.
[11] P. Bargueño, E. C. Vagenas, “Semiclassical corrections to black hole entropy and the generalized uncertainty principle.” Physics Letters B, 742 (2015) 15.
[12] S. Gangopadhyay, A. Dutta, A. Saha, “Generalized uncertainty principle and black hole thermodynamics.” General Relativity & Gravitaion 46 (2014) 1661.
[13] A. Farag Ali, M. Faizal, M. M. Khalil, “Remnants of Black Rings from Gravity’s Rainbow.” JHEP 1412 (2014) 159.
[14] S. H. Hendi and M. Faizal, “Black holes in Gauss-Bonnet gravity’s rainbow.” Physical Review D, 92 (2015) 044027.
[15] M. Mirtorabi, S. Miraboutalebi A. A. Masoudi and L. Farhang Matin, “Quantum gravity modifications of the relativistic ideal gas thermodynamics.” Physica A, 506 (2018) 602.
[16] B. Vakili and M. A. Gorji. “Thermostatistics with minimal length uncertainty relation.” Journal Statistical Mechanics: Theory & Experiment, 2012 (2012) P10013.
[17] A. E. Shalyt-Margolin and J. G. Suarez, “Quantum mechanics at Planck’s scale and density merix.” International J. Modern Physics D, 12 (2003) 265.
[18] A. E. Shalyt-Margolin, A. Y. Tregubovich, “Deformed density matrix and generalized uncertainty relation in thermodynamics.” Modern Physics Letters A, 10 (2004) 71.
[19] S. Miraboutalebi and L. Farhang Matin, “Thermodynamics of canonical ensemble of an ideal gas in presence of Planck-scale effects.” Canadian J. Physics 93 (2015) 1.
[20] L. Farhang Matin and S. Miraboutalebi, “Statistical aspects of harmonic oscillator under minimal length supposition.” Physica A, 425 (2015) 10.
[21] K. Nozari, “Some aspects of Planck scale quantum optics.” Physics Letters B, 629 (2005) 41.
[22] A. F. Ali, S. Das and E. C. Vagenas, “Proposal for testing quantum gravity in the lab.” Physical Revies D, 84 (2011) 044013.
[23] F. Reif, Statistical Physics, Berkeley Physics Course - Volume 5, McGraw-Hill (1975).
[24] R. K. Pathria, Statistical Mechanics - 2nd ed., Butterworth-Heinemann (1997).
[25] W. Greiner, L. Neise and H. Stöcker, Thermodynamics and Statistical Mechanics, Springer-Verlag New York (1997).
[26] P. J. Mohr, B. N. Taylor and D. B. Newell, “CODATA Recommended Values of the Fundamental
Physical Constants.” Review Modern Physics, 84 (2012) 1527.
[27] H. Grote, LIGO Scientific Collaboration. “The status of GEO 600.” Classical Quantum Gravity, 25 (2008) 114043.
[28] B. P. Abbott, et al., “LIGO: the laser interferometer gravitational-wave observatory.” Reports on Progress in Physics, 72 (2009) 076901.
Journal of Interfaces, Thin Films, and Low dimensional systems
Volume 2, Issue 1
November 2018
Pages 99-108