Corrections to the Hawking Tunneling Radiation from MDR

We investigate some aspects of black hole (BH) thermodynamics in the framework of a modified dispersion relation. We calculate a minimal length and a maximal momentum to find a relation between spacetime dimensions and the presence of logarithmic prefactor in the black hole entropy relation. We show that the logarithmic prefactor appears not only in an even number of dimensions but also in an odd number of dimensions. In addition, the sign of the logarithmic factor is different for positive values of α in all dimensions. Using the corrected entropy, the black hole radiation probability is calculated in the tunneling formalism, which is corrected up to the same order of the Planck length and shows a more probable quantum tunneling.     

Photon Gas Thermodynamics in Noncommutative Momentum Spaces

In this paper, we study thermodynamical properties of the extreme relativistic gases in canonical ensembles in non-commutative momentum spaces. In this regards, we exactly calculate the modified partition function, Helmholtz free energy, internal energy, entropy, heat capacity and the thermal pressure in the momentum spaces. Moreover, we conclude at high temperature limits due to the decreasing of the number of micro-states, these quantities reach to maximal bounds which do not exist in standard cases and it concludes that at the presence of gravity for both micro-canonical and canonical ensembles, the internal energy and the entropy tend to these upper bounds.