Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: H-Theorem and Generalized Entropies Within the Framework of Non Linear
  Kinetics   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.

18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th