Relativistic thermodynamics with an invariant energy scale

Das, Sudipta; Ghosh, Subir; Roychowdhury, Dibakar

doi:10.1103/physrevd.80.125036

Cited by 28 publications

(32 citation statements)

References 41 publications

(47 reference statements)

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“…Since statistical mechanics plays an important role in understanding a system consisting of large number of particles, it is reasonable to assume that a study of statistical mechanics of these compact systems in the background of a non-commutative spacetime will be a viable option to understand the Planck scale physics. The effect of Planck scale physics, especially due to the presence of minimal length, in statistical mechanics has been reported by many in the literature [2][3][4][5][6][7][8][9]. Compact stars appears to be a potential source to study the effects of non-commutativity on statistical mechanics, due to its accessibility for observation.…”

Section: Introductionmentioning

confidence: 95%

Compact stars in quantum spacetime

Harikumar

Zuhair

2018

J. Phys. Commun.

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We derive bounds on the deformation parameter of the κ-spacetime by analyzing the effect of noncommutativity on astrophysical model. We study compact stars, taken to be degenerate Fermi gas, in non-commutative spacetime. Using tools of statistical mechanics, we derive the degeneracy pressure of the compact star in κ-spacetime and from the hydrostatic equilibrium conditions we obtain a bound on the deformation parameter. We independently derive this bound using generalized uncertainty principle, which is a characteristic feature of quantum gravity approaches, strengthening the bound obtained.

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Section: Introductionmentioning

confidence: 95%

Compact stars in quantum spacetime

Harikumar

Zuhair

2018

J. Phys. Commun.

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“…In theories with minimal length that formulated on the reduced (non-relativistic) phase space such as generalized uncertainty principle [21], noncommutative reduced phase spaces [22] and polymerized phase spaces [23], always one of the phase space measure or the dispersion relation is modified (it depends on what one prefers to work, in canonical (Darboux) or noncanonical charts on the reduced phase space [16,24,25]). In deformed special relativity theories such as the DSR models, depending on the coordinate that one implements, both the measure and the dispersion relation can be simultaneously modified [26,27]. Using the deformed Hamiltonian constraint (4) and substituting the invariant measure (2) into the definition (12), the canonical partition function for the photon gas in cosmological coordinatization of dS momentum space takes the form…”

Section: Statistical Mechanicsmentioning

confidence: 99%

Photon gas thermodynamics in dS and AdS momentum spaces

et al. 2016

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In this paper, we study thermostatistical properties of a photon gas in the framework of two deformed special relativity models defined by the cosmological coordinatizations of the de Sitter (dS) and anti-de Sitter (AdS) momentum spaces. The dS model is a doubly special relativity theory in which an ultraviolet length scale is invariant under the deformed Lorentz transformations. For the case of AdS model, however, the Lorentz symmetry breaks at the high energy regime. We show that the existence of a maximal momentum in dS momentum space leads to maximal pressure and temperature at the thermodynamical level while maximal internal energy and entropy arise for the case of the AdS momentum space due to the existence of a maximal kinematical energy. These results show the thermodynamical duality of these models much similar to their well-known kinematical duality.

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“…Some attempts have been made in this direction to study the different statistical systems in the context of DSR theories (see Refs. [16,17]). But, here, we would like to generally formulate the statistical mechanics of DSR theories in a more systematic way.…”

Section: Statistical Mechanics: Invariant Measurementioning

confidence: 99%

“…Thermodynamics of some statistical systems in the DSR framework are also studied in Ref. [17]. It is however natural to expect that some fundamental aspects of the early universe thermodynamics may be addressed in the DSR setup.…”

Section: Introductionmentioning

confidence: 99%

Early universe thermostatistics in curved momentum spaces

Gorji¹,

Hosseinzadeh²,

Nozari³

et al. 2016

Phys. Rev. D

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The theories known as doubly special relativity are introduced in order to take into account an observer-independent length scale and the speed of light in the framework of special relativity. These theories can be generally formulated on the de Sitter and also recently proposed anti-de Sitter momentum spaces. In the context of these theories, we study the statistical mechanics and to do this, we consider the natural measure on the corresponding extended phase space. The invariant measure on the space of distinct microstates is obtained by restriction of the natural measure of the extended phase space to the physical phase space through the disintegration theorem. Having the invariant measure, one can study the statistical mechanics in an arbitrary ensemble for any doubly special relativity theory. We use the constructed setup to study the statistical properties of four doubly special relativity models. Applying the results to the case of early universe thermodynamics, we show that one of these models that is defined by the cosmological coordinatization of anti-de Sitter momentum space, implies a finite total number of microstates. Therefore, without attribution to any ensemble density and quite generally, we obtain entropy and internal energy bounds for the early radiation dominated universe. We find that while these results cannot be supported by the standard Friedmann equations, they indeed are in complete agreement with the nonsingular effective Friedmann equations that arise in the context of loop quantum cosmology.

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Relativistic thermodynamics with an invariant energy scale

Cited by 28 publications

References 41 publications

Compact stars in quantum spacetime

Compact stars in quantum spacetime

Photon gas thermodynamics in dS and AdS momentum spaces

Early universe thermostatistics in curved momentum spaces

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