# The $H$-theorem in $\kappa$-statistics: influence on the molecular chaos hypothesis

Authors
Type
Published Article
Publication Date
Jan 24, 2006
Submission Date
Nov 09, 2005
Identifiers
DOI: 10.1016/j.physleta.2005.11.056
arXiv ID: cond-mat/0511228
Source
arXiv
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 $\kappa\to 0$.