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This paper addresses the effect of generalized uncertainty principle, emerged by a different approaches of quantum gravity within Planck scale, on thermodynamic properties of photon, nonrelativistic ideal gases and degenerate fermions. A modification in pressure, particle number and energy density are calculated. Astrophysical objects such as main sequence stars and white dwarfs are examined and discussed as an application. A modification in Lane-Emden equation due to a change in a polytropic relation caused by the presence of quantum gravity, is investigated. The applicable range of quantum gravity parameters is estimated. The bounds in the perturbed parameters are relatively large but it may be considered reasonable values in the astrophysical regime.

Various frameworks of quantum gravity predict a modification in the Heisenberg uncertainty principle to a so-called generalized uncertainty principle (GUP). Introducing quantum gravity effect makes a considerable change in the density of states inside the volume of the phase space which changes the statistical and thermodynamical properties of any physical system. In this paper we investigate the modification in thermodynamic properties of ideal gases and photon gas. The partition function is calculated and using it we calculated a considerable growth in the thermodynamical functions for these considered systems. The growth may happen due to an additional repulsive force between constitutes of gases which may be due to the existence of GUP, hence predicting a considerable increase in the entropy of the system. Besides, by applying GUP on an ideal gas in a trapped potential, it is found that GUP assumes a minimum measurable value of thermal wavelength of particles which agrees with discrete nature of the space that has been derived in previous studies from the GUP.

This paper addresses the effect of a generalized uncertainty principle produced by different approaches of quantum gravity within the Planck scale on statistical and thermodynamical properties of ideal fermion and boson gases. The partition function and some thermodynamical properties are investigated. The Bose-Einstein condensation and the ground state properties of fermion gases are also considered. The target approach is extended to a white dwarf as an application. The modified mass-radius relation is calculated. A decrease in the pressure of degenerate fermions due to the presence of quantum gravity leads to a contraction in the star radius. It is also found that the gravity background does not result in any change in white dwarf stability.

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