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The entropy production paradox for fractional diffusion

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Published/Copyright: March 20, 2023
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Journal of Non-Equilibrium Thermodynamics
From the journal Journal of Non-Equilibrium Thermodynamics Volume 48 Issue 2

Abstract

Dispersive diffusion and wave propagation seem to be unconnected and fundamentally different evolution equations. In the context of anomalous diffusion however modeling approaches based on fractional diffusion equations have been presented, which allow to build a continuous bridge between the two regimes. The transition from irreversible dispersive diffusion to reversible wave propagation shows an unexpected increase in entropy production. This seemingly paradoxical behavior of fractional diffusion is reviewed and compared to the behavior of a tree-based diffusion model.

Keywords: entropy; entropy production paradox; fractional diffusion equations; space-fractional diffusion; time-fractional diffusion
Corresponding author: Karl Heinz Hoffmann, Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany, E-mail:

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2023-02-15
Accepted: 2023-03-05
Published Online: 2023-03-20
Published in Print: 2023-04-28

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Special Issue Articles of the International Workshop on Non-Equilibrium Thermodynamics IWNET 2022 edited by Henning Struchtrup
  3. Editorial
  4. Multiscale theory
  5. The entropy production paradox for fractional diffusion
  6. On small local equilibrium systems
  7. Regular Research Articles
  8. Nonlinear dynamics of blood passing through an overlapped stenotic artery with copper nanoparticles
  9. Maximum ecological function performance for a three-reservoir endoreversible chemical pump
  10. Are all chemical reactions in principle reversible? Thermodynamic distinction between “conceptually complete” and “practically complete” reactions
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https://doi.org/10.1515/jnet-2023-0020
Keywords for this article
entropy; entropy production paradox; fractional diffusion equations; space-fractional diffusion; time-fractional diffusion

Articles in the same Issue

  1. Frontmatter
  2. Special Issue Articles of the International Workshop on Non-Equilibrium Thermodynamics IWNET 2022 edited by Henning Struchtrup
  3. Editorial
  4. Multiscale theory
  5. The entropy production paradox for fractional diffusion
  6. On small local equilibrium systems
  7. Regular Research Articles
  8. Nonlinear dynamics of blood passing through an overlapped stenotic artery with copper nanoparticles
  9. Maximum ecological function performance for a three-reservoir endoreversible chemical pump
  10. Are all chemical reactions in principle reversible? Thermodynamic distinction between “conceptually complete” and “practically complete” reactions
  11. New formulation of the Navier–Stokes equations for liquid flows
  12. Conservatively perturbed equilibrium in multi-route catalytic reactions
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