Quantum gravity modifications of the relativistic ideal gas thermodynamics

Mirtorabi, M.; Miraboutalebi, S.; Masoudi, A. A.; Matin, Laleh Farhang

doi:10.1016/j.physa.2018.04.081

Cited by 15 publications

(15 citation statements)

References 32 publications

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“…This observation comes to confirm the recently obtained result with Perivolaropoulos's algebra [35]. In contrast with the obtained results in the presence of a minimal length, [21,22,23,24,25,26], the ordinary internal energy is shifted at the first order of deformed parameter and led to its decreasing. Thus, the specific heat C remains also unchanged and is given by…”

Section: 1supporting

confidence: 90%

“…The logarithm corrections induced by these quantities are consistent with the ones obtained at the extremal limit of black holes [17,18,19,20] due to the high effectiveness of quantum fluctuation [38]. To confirm these results, we compared our results with those of the minimal length formalism, available in the literature [21,22,23,24,25,26]. On this basis, it is shown that both scenarios are fundamentally different.…”

Section: Discussionsupporting

confidence: 75%

“…This situation perfectly fits with the obtained results at the extremal limit of a black hole geometry [17,18,19,20]. Comparing these consequences with those of minimal length measurement [21,22,23,24,25,26], show that the effects of both measurements are fundamentally different. In fact, the minimal length formalism shifts quadratically the thermodynamic quantities at the order of the deformed parameter β GU P .…”

Section: Introductionsupporting

confidence: 86%

“…Comparing these results with the analogous obtained in the minimal length scenarios [21,22,23,24,25,26] show that, the effect of the maximal length in this framework and that of the minimal length are fundamentally different. In fact, the minimal length induces a weak graviton localization while the maximal length in this context induces a strong graviton localization.…”

Section: 1mentioning

confidence: 66%

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Thermodynamics of Ideal Gas at Planck Scale with Strong Quantum Gravity Measurement

Lawson¹

2021

Preprint

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More recently in J. Phys. A: Math. Theor. 53, 115303 (2020), we have introduced a set of noncommutative algebra that describes the space-time at the Planck scale. The interesting significant result we found is that the generalized uncertainty principle induced a maximal length of quantum gravity which has different physical implications to the one of generalized uncertainty principle with minimal length. The emergence of a maximal length in this theory revealed strong quantum gravitational effects at this scale and predicted the detection of gravity particles with low energies. To make evidence of these predictions, we study the dynamics of a free particle confined in an infinite square well potential in one dimension of this space. Since the effects of quantum gravity are strong in this space, we show that the energy spectrum of this system is weakly proportional to the ordinary one of quantum mechanics free of the theory of gravity. The states of this particle exhibit proprieties similar to the standard coherent states which are consequences of quantum fluctuation at this scale. Then, with the spectrum of this system at hand, we analyze the thermodynamic quantities within the canonical and micro-canonical ensembles of an ideal gas made up of N indistinguishable particles at the Planck scale. The results show a complete consistency between both statistical descriptions. Furthermore, a comparison with the results obtained in the context of minimal length scenarios and black hole theories indicates that the maximal length in this theory induces logarithmic corrections of deformed parameters which are consequences of a strong quantum gravitational effect.

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Section: 1supporting

confidence: 90%

Section: Discussionsupporting

confidence: 75%

Section: Introductionsupporting

confidence: 86%

Section: 1mentioning

confidence: 66%

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Thermodynamics of Ideal Gas at Planck Scale with Strong Quantum Gravity Measurement

Lawson¹

2021

Preprint

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“…Based on minimum observable length, the quantum gravity implications on the statistical properties of ideal gases have been investigated in many studies, see, e.g., [42][43][44][45] and references therein. In the framework of GUP: (i) deformed density of states and an improved definition of the statistical entropy have been introduced in [46,47], (ii) Maxwell-Boltzmann statistics have been investigated in [48], and (iii) employing Maxwell-Boltzmann statistics, the thermodynamics of relativistic ideal gas has also been analyzed in [49]. In the same manner, there have been some studies on the deformation of statistical concepts in the EUP framework [50,51].…”

Section: Introductionmentioning

confidence: 99%

A Note on Effects of Generalized and Extended Uncertainty Principles on Jüttner Gas

2021

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In recent years, the implications of the generalized (GUP) and extended (EUP) uncertainty principles on Maxwell–Boltzmann distribution have been widely investigated. However, at high energy regimes, the validity of Maxwell–Boltzmann statistics is under debate and instead, the Jüttner distribution is proposed as the distribution function in relativistic limit. Motivated by these considerations, in the present work, our aim is to study the effects of GUP and EUP on a system that obeys the Jüttner distribution. To achieve this goal, we address a method to get the distribution function by starting from the partition function and its relation with thermal energy which finally helps us in finding the corresponding energy density states.

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The Effects of the Modified (Anti-)Snyder Model on the Thermodynamic Properties of an Ideal Gas

2020

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Quantum gravity modifications of the relativistic ideal gas thermodynamics

Cited by 15 publications

References 32 publications

Thermodynamics of Ideal Gas at Planck Scale with Strong Quantum Gravity Measurement

Thermodynamics of Ideal Gas at Planck Scale with Strong Quantum Gravity Measurement

A Note on Effects of Generalized and Extended Uncertainty Principles on Jüttner Gas

The Effects of the Modified (Anti-)Snyder Model on the Thermodynamic Properties of an Ideal Gas

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