Tsallis Relative Entropy and Anomalous Diffusion

Entropy

Janett Prehl¹  Christopher Essex² 

[1] Institute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, Germany; E-Mail:;Department of Applied Mathematics, University of Western Ontario, Middlesex College, London, ON, N6A 5B7, Canada; E-Mail:

关键词: space-fractional diffusion equation;    stable distribution;    Kullback–Leibler entropy;    Tsallis relative entropy;   

DOI  :  10.3390/e14040701

来源: mdpi

【 摘 要 】

In this paper we utilize the Tsallis relative entropy, a generalization of the Kullback–Leibler entropy in the frame work of non-extensive thermodynamics to analyze the properties of anomalous diffusion processes. Anomalous (super-) diffusive behavior can be described by fractional diffusion equations, where the second order space derivative is extended to fractional orderthe (half) wave equation is given. These fractional diffusion equations are solved by so-called stable distributions, which exhibit heavy tails and skewness. In contrast to the Shannon or Tsallis entropy of these distributions, the Kullback and Tsallis relative entropy, relative to the pure diffusion case, induce a natural ordering of the stable distributions consistent with the ordering implied by the pure diffusion and wave limits.

【 授权许可】

CC BY   
© 2012 by the authors; licensee MDPI, Basel, Switzerland.