Nonlinear differential equations based on nonextensive Tsallis entropy and physical applications

R. S. Mendes; I. T. Pedron

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arXiv · cond-mat/9904023

Nonlinear differential equations based on nonextensive Tsallis entropy and physical applications

R. S. Mendes·I. T. Pedron

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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.

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R. S. Mendes, I. T. Pedron. 1999-04-01. Nonlinear differential equations based on nonextensive Tsallis entropy and physical applications. https://arxiv.org/abs/cond-mat/9904023

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