Blackbody radiation, kappa distribution and superstatistics

Abstract

In this work we apply superstatistics, in a rather novel way, to derive the blackbody radiation laws in the context of the kappa distribution. Superstatistics incorporates automatically an important aspect of the kappa distribution i.e. the correlations between non-interacting degrees of freedom; this is actually a feature of any stationary non-Boltzmannian distribution derived by superstatistics. The correlations between photons in the same state affect the modified Planck and Wien laws. The correlations between photons of different states affect the fluctuations of the radiated energy, inducing very large fluctuations unless the kappa index is fairly large (i.e. near to the Boltzmannian limit), thereby compromising the very notion of stationarity. It is also shown that the Einstein absorption/emission coefficients are left intact, under the plausible assumption that the system matter-radiation obeys the given non-Boltzmannian distribution. The first-order correction to the Planck’s law near the Boltzmannian limit is deduced, and compared with the residual spectrum of the cosmic microwave background radiation from the FIRAS-COBE project data; the modified law cannot account for the residuals. No thermodynamic/entropic arguments are employed in this work.