Olbert’s Kappa Fermi and Bose Distributions

The quantum version of Olbert's kappa distribution applicable to fermions is obtained. Its construction straightforward but requires recognition the differences in nature states separated by Fermi momenta. complement, bosonic also given, as procedure how construct a hypothetical kappa-anyon distribution. At very low temperature degenerate yields kappa-modified ordinary energy and momentum. We provide Olbert-generalized expressions Olbert-Fermi partition function entropy which may serve determining all relevant statistical mechanical quantities. Possible applications are envisaged condensed matter physics, possibly plasmas, dense astrophysical objects like interior state terrestrial planets, neutron stars, magnetars where effects come into play, dominate microscopic scale have macroscopic consequences.