Motivated by the doubly special relativity theories and noncommutative spacetime structures, thermodynamical properties of the photon gas in a phase space with compact spatial momentum space is studied. At the high temperature limit, the upper bounds for the internal energy and entropy are obtained which are determined by the size of the compact spatial momentum space. The maximum internal energy turns out to be of the order of the Planck energy and the entropy bound is then determined by the factor $\big(V/l_{_{\rm Pl}}^3\big)$ through the relevant identification of the size of the momentum space with Planck scale. The entropy bound is very similar to the case of Bekenstein-Hawking entropy of black holes and suggests that thermodynamics of black holes may be deduced from a saturated state in the framework of a full quantum gravitational statistical mechanics.Comment: 11 pages, 3 figure

Black hole thermodynamics is corrected in the presence of quantum gravity effects. Some phenomenological aspects of quantum gravity proposal can be addressed through generalized uncertainty principle (GUP) which provides a perturbation framework to perform required modifications of the black hole quantities. In this paper, we consider the effects of both a minimal measurable length and a maximal momentum on the thermodynamics of TeV-scale black holes. We then extend our study to the case that there are all natural cutoffs as minimal length, minimal momentum, and maximal momentum simultaneously. We also generalize our study to the model universes with large extra dimensions (LED). In this framework existence of black holes remnants as a possible candidate for dark matter is discussed. We study probability of black hole production in the Large Hadronic Collider (LHC) and we show this rate decreasing for sufficiently large values of the GUP parameter.

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In this paper, using a deformed algebra [Formula: see text] which is originated from various theories of gravity, we study thermodynamical properties of quantum black holes (BHs) in canonical ensembles. We exactly calculate the modified internal energy, entropy and heat capacity. Moreover, we investigate a tunneling mechanism of massless particle in phase space. In this regard, the tunneling radiation of BH receives new corrections and the exact radiant spectrum is no longer precisely thermal. In addition, we show that our results are compatible with other quantum gravity (QG) approaches.