Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime
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 th...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2018-11-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/20/11/881 |
| _version_ | 1798038186035773440 |
|---|---|
| author | Karl Heinz Hoffmann Kathrin Kulmus Christopher Essex Janett Prehl |
| author_facet | Karl Heinz Hoffmann Kathrin Kulmus Christopher Essex Janett Prehl |
| author_sort | Karl Heinz Hoffmann |
| collection | DOAJ |
| description | 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 <i>increase</i> 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. |
| first_indexed | 2024-04-11T21:36:47Z |
| format | Article |
| id | doaj.art-932bddfbd24f4d5f92abed942d325dc1 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T21:36:47Z |
| publishDate | 2018-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-932bddfbd24f4d5f92abed942d325dc12022-12-22T04:01:43ZengMDPI AGEntropy1099-43002018-11-01201188110.3390/e20110881e20110881Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional RegimeKarl Heinz Hoffmann0Kathrin Kulmus1Christopher Essex2Janett Prehl3Institute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, GermanyInstitute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, GermanyDepartment of Applied Mathematics, University of Western Ontario, Middlesex College, London, ON N6A 5B7, CanadaInstitute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, GermanyThe 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 <i>increase</i> 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.https://www.mdpi.com/1099-4300/20/11/881entropy production paradoxentropyfractional diffusion |
| spellingShingle | Karl Heinz Hoffmann Kathrin Kulmus Christopher Essex Janett Prehl Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime Entropy entropy production paradox entropy fractional diffusion |
| title | Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime |
| title_full | Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime |
| title_fullStr | Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime |
| title_full_unstemmed | Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime |
| title_short | Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime |
| title_sort | between waves and diffusion paradoxical entropy production in an exceptional regime |
| topic | entropy production paradox entropy fractional diffusion |
| url | https://www.mdpi.com/1099-4300/20/11/881 |
| work_keys_str_mv | AT karlheinzhoffmann betweenwavesanddiffusionparadoxicalentropyproductioninanexceptionalregime AT kathrinkulmus betweenwavesanddiffusionparadoxicalentropyproductioninanexceptionalregime AT christopheressex betweenwavesanddiffusionparadoxicalentropyproductioninanexceptionalregime AT janettprehl betweenwavesanddiffusionparadoxicalentropyproductioninanexceptionalregime |