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Tsallis and Rényi entropies in fractional diffusion and entropy production

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  • Essex, Christopher
  • Schulzky, Christian
  • Franz, Astrid
  • Hoffmann, Karl Heinz

Abstract

The entropy production rate for fractional diffusion processes using Shannon entropy was calculated previously, which showed an apparently counter intuitive increase with the transition from dissipative diffusion behaviour to reversible wave propagation. Rényi and Tsallis entropies, which have an additional parameter q generalizing the Shannon case (q=1), are shown here to have similar counter intuitive behaviours. However, the issue can be successfully treated in exactly the same manner as with Shannon entropy for q being not too large (i.e., generalizations near the Shannon case), whereas for larger q the Rényi and Tsallis entropies behave in a different way.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:284:y:2000:i:1:p:299-308
    DOI: 10.1016/S0378-4371(00)00174-6
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    References listed on IDEAS

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    1. Metzler, Ralf & Glöckle, Walter G. & Nonnenmacher, Theo F., 1994. "Fractional model equation for anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 211(1), pages 13-24.
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    Cited by:

    1. Kulmus, Kathrin & Essex, Christopher & Prehl, Janett & Hoffmann, Karl Heinz, 2019. "The entropy production paradox for fractional master equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1370-1378.
    2. 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.

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