The $H$-theorem in $κ$-statistics: influence on the molecular chaos hypothesis

Abstract

We rediscuss recent derivations of kinetic equations based on the Kaniadakis' entropy concept. Our primary objective here is to derive a kinetical version of the second law of thermodynamycs in such a $κ$-framework. To this end, we assume a slight modification of the molecular chaos hypothesis. For the $H_κ$-theorem, it is shown that the collisional equilibrium states (null entropy source term) are described by a $κ$-power law extension of the exponential distribution and, as should be expected, all these results reduce to the standard one in the limit $κ\to 0$.