Diffusive mixing and Tsallis entropy

O'Malley, Daniel; Vesselinov, Velimir V.; Cushman, John H.

doi:10.1103/PhysRevE.91.042143

Title: Diffusive mixing and Tsallis entropy

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Abstract

Brownian motion, the classical diffusive process, maximizes the Boltzmann-Gibbs entropy. The Tsallis q-entropy, which is non-additive, was developed as an alternative to the classical entropy for systems which are non-ergodic. 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. In addition, 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:

O'Malley, Daniel ^[1]; Vesselinov, Velimir V. ^[1]; Cushman, John H. ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Purdue Univ., West Lafayette, IN (United States)

Publication Date:: Wed Apr 29 00:00:00 EDT 2015

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1236601

Alternate Identifier(s):: OSTI ID: 1182810

Report Number(s):: LA-UR-14-28031
Journal ID: ISSN 1539-3755; PLEEE8

Grant/Contract Number:: EAR1314828; AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

Additional Journal Information:: Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print); Journal Volume: 91; Journal Issue: 4; Journal ID: ISSN 1539-3755

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 58 GEOSCIENCES

Citation Formats


                    O'Malley, Daniel, Vesselinov, Velimir V., and Cushman, John H. Diffusive mixing and Tsallis entropy.  United States: N. p., 2015. 
Web.  doi:10.1103/PhysRevE.91.042143.

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                    O'Malley, Daniel, Vesselinov, Velimir V., & Cushman, John H. Diffusive mixing and Tsallis entropy.  United States.  https://doi.org/10.1103/PhysRevE.91.042143

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                    O'Malley, Daniel, Vesselinov, Velimir V., and Cushman, John H. Wed .  
"Diffusive mixing and Tsallis entropy".  United States.  https://doi.org/10.1103/PhysRevE.91.042143.  https://www.osti.gov/servlets/purl/1236601.

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@article{osti_1236601,

  title        = {Diffusive mixing and Tsallis entropy},

  author       = {O'Malley, Daniel and Vesselinov, Velimir V. and Cushman, John H.},

  abstractNote = {Brownian motion, the classical diffusive process, maximizes the Boltzmann-Gibbs entropy. The Tsallis q-entropy, which is non-additive, was developed as an alternative to the classical entropy for systems which are non-ergodic. 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. In addition, the distribution of this coefficient is derived as a function of q for 1 < q < 3. Applications to transport in porous media are considered.},

  doi          = {10.1103/PhysRevE.91.042143},

  journal      = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)},

  number       = 4,

  volume       = 91,

  place        = {United States},

  year         = {Wed Apr 29 00:00:00 EDT 2015},

  month        = {Wed Apr 29 00:00:00 EDT 2015}

}

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