  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.
