Blackbody Radiation in $q$-deformed Statistics

TL;DR

This paper explores how $q$-deformed statistics modify blackbody radiation laws, revealing shifts in spectral peaks and displacement laws that depend on the deformation parameter $q$, thus providing a more generalized statistical framework.

Contribution

It introduces a $q$-deformed statistical approach to blackbody radiation, analyzing the impact of the deformation parameter on spectral properties and displacement laws.

Findings

Peak of energy spectrum shifts to higher frequencies with increasing $q$

The product $ u_m T$ varies with $q$, indicating a modified Wien's law

Deformation parameter $q$ influences the spectral distribution and law constants

Abstract

More general canonical ensemble which gives rise the generalized statistics or $q$-deformed statistics can represent the realistic scenario than the ideal one, with proper parameter sets involved. We study the Planck's law of blackbody radiation, Wein's and Rayleigh-Jeans radiation formulae from the point of view of $q$-deformed statistics. We find that the blackbody energy spectrum curve for a given temperature $T$ corresponding to different $q$ values differs from each other: the location of the peak(i.e. $\nu_m$) of the energy distribution $u_\nu$ (corresponding to different $q$ ) shifted towards higher $\nu$ for higher $q$. From the $q$-deformed Wein's displacement law, we find that $\lambda_m T$ varies from $0.0029~\rm{m~K}$ to $0.0017~\rm{m~K}$ as the deformation parameter $q$ varies from $1.0$(undeformed) to $1.1$(deformed).