# On the applicability of $\kappa$-distributions

## TL;DR

This paper examines the limitations of the standard $5$-distribution in physical modeling, highlighting issues with superluminal particles at low $5$ values, and proposes a regularized version to eliminate unphysical effects.

## Contribution

It introduces a regularized $5$-distribution that avoids unphysical superluminal contributions present in the standard form.

## Key findings

- Standard $5$-distribution predicts superluminal particles for $5<2$.
- Regularized $5$-distribution removes unphysical superluminal effects.
- The regularized distribution maintains physical consistency in thermodynamical descriptions.

## Abstract

The standard (non-relativistic) $\kappa$-distribution is widely used to fit data and to describe macroscopic thermodynamical behavior, e.g.\ the pressure (temperature) as the second moment of the distribution function. By contrast to a Maxwellian distribution, for small relevant values $\kappa < 2$ there exists a significant, but unphysical contribution to the pressure from unrealistic, superluminal particles with speeds exceeding the speed of light. Similar concerns exist for the entropy. We demonstrate here that by using the recently introduced regularized $\kappa$-distribution one can avoid such unphysical behaviour.