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The superdiffusion entropy production paradox in the space-fractional case for extended entropies

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  • Prehl, J.
  • Essex, C.
  • Hoffmann, K.H.

Abstract

Contrary to intuition, entropy production rates grow as reversible, wave-like behavior is approached. This paradox was discovered in time-fractional diffusion equations. It was found to persist for extended entropies and for space-fractional diffusion as well. This paper completes the possibilities by showing that the paradox persists for Tsallis and Rényi entropies in the space-fractional case. Complications arising due to the heavy tail solutions of space-fractional diffusion equations are discussed in detail.

Suggested Citation

  • Prehl, J. & Essex, C. & Hoffmann, K.H., 2010. "The superdiffusion entropy production paradox in the space-fractional case for extended entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(2), pages 215-224.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:2:p:215-224
    DOI: 10.1016/j.physa.2009.09.009
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    References listed on IDEAS

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    1. Essex, Christopher & Schulzky, Christian & Franz, Astrid & Hoffmann, Karl Heinz, 2000. "Tsallis and Rényi entropies in fractional diffusion and entropy production," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 299-308.
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    Cited by:

    1. Reem Abdullah Aljethi & Adem Kılıçman, 2023. "Derivation of the Fractional Fokker–Planck Equation for Stable Lévy with Financial Applications," Mathematics, MDPI, vol. 11(5), pages 1-13, February.

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