AUTHOR=Treumann R. A. , Baumjohann Wolfgang 

TITLE=Olbert’s Kappa Fermi and Bose Distributions

JOURNAL=Frontiers in Physics

VOLUME=Volume 9 - 2021

YEAR=2021

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.672836

DOI=10.3389/fphy.2021.672836

ISSN=2296-424X

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