Kappa distributions in the framework of superstatistics

The kappa distribution of velocities is frequently found instead of the Maxwellian distribution in collisionless plasmas present in Earth’s magnetosphere, the solar wind among other contexts where particles do not reach thermal equilibrium. Although the origin of these distributions is sometimes explained by means of non-extensive statistics, they can also be recovered using alternative frameworks such as superstatistics, providing a closer connection with probability theory. In this work we take this approach and derive the multi-particle and single-particle kappa distributions from superstatistics while taking into account the scale invariance property of the superstatistical temperature distribution. The formalism presented here emphasizes the usefulness of superstatistics in the computation of expectation values under kappa distributions. Some consequences of a superstatistical interpretation of kappa distributions are also discussed, such as the connection between correlations and temperature uncertainty, the meaning of the superstatistical temperature and the entropy of kappa-distributed plasmas.