Equilibrium properties of blackbody radiation with an ultraviolet energy cut-off

Abstract

We study various equilibrium thermodynamic properties of blackbody radiation (i.e. a photon gas) with an ultraviolet energy cut-off. We find that the energy density, specific heat etc. follow usual acoustic phonon dynamics as have been well studied by Debye. Other thermodynamic quantities like pressure, entropy etc. have also been calculated. The usual Stefan–Boltzmann law gets modified. We observe that the values of the thermodynamic quantities with the energy cut-off is lower than the corresponding values in the theory without any such scale. The phase-space measure is also expected to get modified for an exotic spacetime appearing at Planck scale, which in turn leads to the modification of Planck energy density distribution and the Wien’s displacement law. We found that the non-perturbative nature of the thermodynamic quantities in the SR limit (for both unmodified and modified cases), due to nonanalyticity of the leading term, is a general feature of the theory accompanied with an ultraviolet energy cut-off. We have also discussed the possible modification in the case of Big Bang and the Stellar objects and have suggested a table top experiment for verification in effective low energy case.