Thermodynamics of a photon gas with an invariant energy scale

The quantum gravity framework motivates us to find new theories in which an observer-independent finite energy upper bound (preferably Planck energy) exists. We have studied the modifications in the thermodynamical properties of a photon gas in such a scenario where we have an invariant energy scale. We show that the density of states and the entropy in such a framework are less than the corresponding quantities in Einstein’s special relativity theory. This result can be interpreted as a consequence of the deformed Lorentz symmetry present in the particular model we have considered.

Figure 1

Plot of entropy of photon $S$ against temperature $T$ for both in the SR theory and in our case; the dashed line corresponds to the SR theory result and the thick line represents the corresponding quantity in our result. We have used the Planck units and the corresponding parameters take the following values $\kappa =10000$, $k_B=1$, $N=10000$, $V=0.01$, $h=1$ in this plot as well as in all other plots in the paper. In this scale, $T=10000$ is the Planck temperature.

Figure 2

Plot of internal energy of photon $U$ against temperature $T$ for both in the SR theory and MS scenario; the dashed line corresponds to the SR theory result and the thick line represents the quantity in the MS model we considered here.

Figure 3

Plot of specific heat of photon $C_V$ against temperature $T$ for both in the SR theory and MS scenario; the dashed line corresponds to the SR theory result and the thick line represents the quantity in the MS model we considered here.