Olbert's kappa Fermi and Bose distributions

TL;DR

This paper introduces a quantum Olbert's kappa distribution for fermions and bosons, extending statistical mechanics tools to systems with non-standard distributions, with potential applications in condensed matter and astrophysics.

Contribution

It presents the first derivation of a quantum Olbert's kappa distribution for fermions and bosons, including partition functions and entropy expressions.

Findings

Derived the quantum Olbert's kappa fermion distribution.

Provided expressions for partition function and entropy.

Suggested applications in astrophysics and condensed matter.

Abstract

The quantum version of Olbert's kappa 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. Its complement, the bosonic version of the kappa distribution is also given, as is the procedure of how to construct a hypothetical kappa-anyon distribution. At very low temperature the degenerate kappa Fermi distribution yields a kappa-modified version of the ordinary degenerate Fermi 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.