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.
On the entropy of plasmas described with regularized $\kappa$-distributions
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abstract
In classical thermodynamics the entropy is an extensive quantity, i.e.\ the sum of the entropies of two subsystems in equilibrium with each other is equal to the entropy of the full system consisting of the two subsystems. The extensitivity of entropy has been questioned in the context of a theoretical foundation for the so-called $\kappa$-distributions, which describe plasma constituents with power-law velocity distributions. We demonstrate here, by employing the recently introduced {\it regularized $\kappa$-distributions}, that entropy can be defined as an extensive quantity even for such power-law-like distributions that truncate exponentially.
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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.