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On the applicability of $\kappa$-distributions
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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.
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Relativistic regularized kappa distributions
The authors define a special relativistic regularized kappa distribution that keeps all moments finite for every positive kappa, while the standard relativistic kappa distribution requires kappa greater than 2 or 3.
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