On the entropy of plasmas described with regularized $\kappa$-distributions

TL;DR

This paper demonstrates that using regularized ppa-distributions, plasma entropy can be considered extensive, even for power-law velocity distributions with exponential truncation, challenging traditional thermodynamic assumptions.

Contribution

It introduces a framework showing entropy remains extensive for regularized ppa-distributions in plasmas, extending thermodynamic principles to non-Maxwellian velocity distributions.

Findings

Entropy is extensive for regularized ppa-distributions.

Power-law velocity distributions with exponential truncation can have well-defined entropy.

The approach bridges classical thermodynamics with non-Maxwellian plasma models.

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.