Hoffmann KH, Kulmus K, Essex C, Prehl J. Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime.
ENTROPY 2018;
20:e20110881. [PMID:
33266605 PMCID:
PMC7512464 DOI:
10.3390/e20110881]
[Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/30/2018] [Revised: 11/08/2018] [Accepted: 11/09/2018] [Indexed: 11/16/2022]
Abstract
The entropy production rate is a well established measure for the extent of irreversibility in a process. For irreversible processes, one thus usually expects that the entropy production rate approaches zero in the reversible limit. Fractional diffusion equations provide a fascinating testbed for that intuition in that they build a bridge connecting the fully irreversible diffusion equation with the fully reversible wave equation by a one-parameter family of processes. The entropy production paradox describes the very non-intuitive increase of the entropy production rate as that bridge is passed from irreversible diffusion to reversible waves. This paradox has been established for time- and space-fractional diffusion equations on one-dimensional continuous space and for the Shannon, Tsallis and Renyi entropies. After a brief review of the known results, we generalize it to time-fractional diffusion on a finite chain of points described by a fractional master equation.
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