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The entropy production paradox for fractional master equations

Author

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  • Kulmus, Kathrin
  • Essex, Christopher
  • Prehl, Janett
  • Hoffmann, Karl Heinz

Abstract

Time-fractional evolution equations for probability distributions provide a means to describe an important class of stochastic processes. Their solutions show features, which are essential in modeling a variety of phenomena in real world applications. One aspect, which has been observed in time-fractional diffusion equations, shows a surprising and unexpected behavior of the entropy production rate induced by these equations. The entropy production rate increases as one moves away from the fully irreversible case, corresponding to classical diffusion. This rate is analyzed for a new class of systems with state spaces that are finite and denumerable. We find that the entropy production paradox reemerges nonetheless, but in a new and unexpected form.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:525:y:2019:i:c:p:1370-1378
    DOI: 10.1016/j.physa.2019.03.114
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    References listed on IDEAS

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    1. Dexter O. Cahoy & Federico Polito & Vir Phoha, 2015. "Transient Behavior of Fractional Queues and Related Processes," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 739-759, September.
    2. 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.
    3. Buonocore, A. & Caputo, L. & Nobile, A.G. & Pirozzi, E., 2014. "Gauss–Markov processes in the presence of a reflecting boundary and applications in neuronal models," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 799-809.
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