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In this article, we discuss some well-known theoretical models where anobserver-independent energy scale or a length scale is present. The presence ofthis invariant scale necessarily deforms the Lorentz symmetry. We studydifferent aspects and features of such theories about how modifications arisedue to this cutoff scale. First we study the formulation of energy-momentumtensor for a perfect fluid in doubly special relativity (DSR), where an energyscale is present. Then we go on to study modifications in thermodynamicproperties of photon gas in DSR. Finally we discuss some models withgeneralized uncertainty principle (GUP).

Effects of a Maximal Energy Scale in Thermodynamics for Photon Gas and Construction of Path Integral