The nonextensive entropy approach versus the stochastic in describing subdiffusion

Details The nonextensive entropy approach versus the stochastic in describing subdiffusion The nonextensive entropy approach versus the stochastic in describing subdiffusion

2012-01-15

arxiv.org/abs/1201.3121v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

We have proposed a new stochastic interpretation of the sudiffusion described by the Sharma-Mittal entropy formalism which generates a nonlinear subdiffusion equation with natural order derivatives. We have shown that the solution to the diffusion equation generated by Gauss entropy (which is the particular case of Sharma-Mittal entropy) is the same as the solution of the Fokker-Planck (FP) equation generated by the Langevin generalised equation where the `long memory effect' is taken into account. The external noise which pertubates the subdiffusion coefficient (occuring in the solution of FP equation) according to the formula $D_\alpha\rightarrow D_\alpha/u$ where $u$ is a random variable described by the Gamma distribution, provides us with solutions of equations obtained from Sharma-Mittal entropy. We have also shown that the parameters $q$ and $r$ occuring in Sharma-Mittal entropy are controlled by the parameters $\alpha$ and $$, respectively.