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 thermodynamics 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 → 0 .