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.