Abstract
Planck scale inspired theories which are also often accompanied with maximum energy and/or momentum scale predict deformed dispersion relations compared to ordinary special relativity and quantum mechanics. In this paper, we resort to the methods of statistical mechanics in order to determine the effects of a deformed dispersion relation along with an upper bound in the partition function that maximum energy and/or momentum scale can have on the thermodynamics of photon gas. We also analyzed two distinct quantum gravity models in this paper.
Highlights
Different quantum gravity approaches such as string theory, loop quantum gravity, noncommutative geometry, doubly special relativity (DSR), generalized uncertainty principle (GUP) suggest the existence of a minimal length scale of the order of Planck length lp = G c3This length and its inverse, the Planck energy Ep, mark thresholds beyond which the old description of spacetime breaks down and qualitatively new phenomena are expected to appear [1]
The thermodynamic quantities in DSR model pick smaller value compared to usual result in that temperature
This is expected in the DSR model, as the dispersion relation is unchanged compared to SR and due to the presence of upper energy scale the total number of microstates becomes less than SR
Summary
EP is the Planck energy and α is a coefficient of order 1, whose precise value depends upon the considered quantum-gravity model, while n, the lowest power in Planck’s length leading to a non-vanishing contribution, is model dependent quantity This type of dispersion relation is observed in loop quantum gravity [5]. We will visit the thermodynamics of photon gas with this deformed dispersion relation, but with maximum energy bound as argued above We will refer this model as model 2 in this paper
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