The $H$-theorem in $\kappa$-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 $\kappa$-framework. To this end, we assume a slight modification of the molecular chaos hypothesis. For the $H_{\kappa }$-theorem, it is shown that the collisional equilibrium states (null entropy source term) are described by a $\kappa$-power law extension of the exponential distribution and, as should be expected, all these results reduce to the standard one in the limit $\kappa \to 0$.

4 pages, eqs. (18) and (22) have been corrected, to appear in Phys. Lett. A

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