  In the present effort we consider the most general non linear particle
kinetics within the framework of the Fokker-Planck picture. We show that the
kinetics imposes the form of the generalized entropy and subsequently we
demonstrate the H-theorem. The particle statistical distribution is obtained,
both as stationary solution of the non linear evolution equation and as the
state which maximizes the generalized entropy. The present approach allows to
treat the statistical distributions already known in the literature in a
unifying scheme. As a working example we consider the kinetics, constructed by
using the $\kappa$-exponential $\exp_{_{\{\kappa\}}}(x)=
(\sqrt{1+\kappa^2x^2}+\kappa x)^{1/\kappa}$ recently proposed which reduces to
the standard exponential as the deformation parameter $\kappa$ approaches to
zero and presents the relevant power law asymptotic behaviour
$\exp_{_{\{\kappa\}}}(x){\atop\stackrel\sim x\to \pm \infty}|2\kappa x|^{\pm
1/|\kappa|}$. The $\kappa$-kinetics obeys the H-theorem and in the case of
Brownian particles, admits as stationary state the distribution
$f=Z^{-1}\exp_{_{\{\kappa\}}}[-(\beta mv^2/2-\mu)]$ which can be obtained also
by maximizing the entropy $S_{\kappa}=\int d^n v [
c(\kappa)f^{1+\kappa}+c(-\kappa)f^{1-\kappa}]$ with $c(\kappa)=-Z^{\kappa}/
[2\kappa(1+\kappa)]$ after properly constrained.
