Abstract
Brownian motion, the classical diffusive process, maximizes the Boltzmann-Gibbs entropy. The Tsallis entropy, which is nonadditive, was developed as an alternative to the classical entropy for systems which are nonergodic. A generalization of Brownian motion is provided that maximizes the Tsallis entropy rather than the Boltzmann-Gibbs entropy. This process is driven by a Brownian measure with a random diffusion coefficient. The distribution of this coefficient is derived as a function of for . Applications to transport in porous media are considered.
- Received 15 October 2014
DOI:https://doi.org/10.1103/PhysRevE.91.042143
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