Planck radiation law and Einstein coefficients reexamined in Kaniadakis $\kappa$ statistics

Blackbody radiation is reconsidered using the counterpart of the Bose-Einstein distribution in the $\kappa$ statistics arising from the Kaniadakis entropy. The generalized Planck radiation law is presented and compared to the usual law, to which it reduces in the limiting case $\kappa \to 0$. Effective Einstein's coefficients of emission and absorption are defined in terms of the Kaniadakis parameter $\kappa$. It is shown that the Kaniadakis statistics keeps unchanged the first Einstein coefficient $A$ while the second coefficient $B$ admits a generalized form within the present theoretical framework.

Figure 1

Variation of the energy density with the frequency, for different values of the Kaniadakis parameter $\kappa =0.00$ (solid line), $0.10$ (dashed line), $0.20$ (dotted line), and $0.30$ (dash-dotted line), with $T=500$ K.

Figure 2

Variation of the ratio $B_{21}/B_{12}$ with the temperature, for different values of the Kaniadakis parameter $\kappa =0.10$ (solid line), $0.50$ (dashed line), and $0.90$ (dotted line), with $\nu ={10}^{14}$ Hz and a given $E_1$.

Figure 3

Variation of the ratio $B_{21}/B_{12}$ with the frequency, for different values of the Kaniadakis parameter $\kappa =0.10$ (solid line), $0.50$ (dashed line), and $0.90$ (dotted line), with $T=1000$ K and a given $E_1$.