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

TL;DR

This paper explores the $H$-theorem within $$-statistics, deriving a kinetic version of the second law of thermodynamics using a modified molecular chaos hypothesis, resulting in $$-power law equilibrium distributions.

Contribution

It introduces a kinetic formulation of the second law in $$-statistics, extending the $H$-theorem with a modified molecular chaos hypothesis and $$-power law equilibria.

Findings

Equilibrium states are described by a $$-power law extension of exponential distributions.

Results reduce to classical cases as $ o 0$.

Derived a $$-version of the $H$-theorem.

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 $\kappa\to 0$.