title: Diffusive mixing and Tsallis entropy.
abstract: Brownian motion, the classical diffusive process, maximizes the Boltzmann-Gibbs entropy. The Tsallis q 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 q for 1<q<3. Applications to transport in porous media are considered.
authors.affiliation: Computational Earth Science, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors.forename: Daniel
authors.initials: D
authors.lastname: O'Malley
authors.affiliation: Computational Earth Science, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors.forename: Velimir V
authors.initials: VV
authors.lastname: Vesselinov
authors.affiliation: Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, West Lafayette, Indiana 47907, USA and Department of Mathematics, Purdue University, West Lafayette, Indiana 47907, USA.
authors.forename: John H
authors.initials: JH
authors.lastname: Cushman