Nonlinear differential equations based on nonextensive Tsallis entropy and physical applications
Statistical Mechanics
2007-05-23 v1
Abstract
A family of nonlinear ordinary differential equations with arbitrary order is obtained by using nonextensive concepts related to the Tsallis entropy. Applications of these equations are given here. In particular, a connection between Tsallis entropy and the one-dimensional correlated anomalous diffusion equation is established. It is also developed explicitly a WKB-like method for second order equations and it is applied to solve approximately a class of equations that contains as a special case the Thomas-Fermi equation for an atom. It is expected that the present ideas can be useful in the discussion of other nonlinear contexts.
Cite
@article{arxiv.cond-mat/9904023,
title = {Nonlinear differential equations based on nonextensive Tsallis entropy and physical applications},
author = {R. S. Mendes and I. T. Pedron},
journal= {arXiv preprint arXiv:cond-mat/9904023},
year = {2007}
}
Comments
No figures; rsmendes@dfi.uem.br; thamar@dfi.uem.br