Diffusion and Kinetic Theory on Very Long Time and Large Space Scales
This paper extends the concept of epitropy, as introduced in previous work, to capture the effects of extreme tail behavior arising naturally over very long time and large space scales. Epitropy has some qualities that parallel entropy, although it is not quite the same. Its function is to capture t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/26/12/1037 |
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| _version_ | 1846104715701518336 |
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| author | Christopher Essex Bjarne Andresen |
| author_facet | Christopher Essex Bjarne Andresen |
| author_sort | Christopher Essex |
| collection | DOAJ |
| description | This paper extends the concept of epitropy, as introduced in previous work, to capture the effects of extreme tail behavior arising naturally over very long time and large space scales. Epitropy has some qualities that parallel entropy, although it is not quite the same. Its function is to capture the effects of a probability distribution function (PDF) having only a finite populated domain, which was introduced to eliminate divergent moment integrals. Unlike entropy, it represents hidden properties from the <i>external</i> (not the internal) that influence other regimes. This paper uses kinetic theory methods to show the necessity of epitropy in order to ensure that divergent moment integrals do not diverge. While on laboratory scales, the issues in question are negligible, we arrive at dynamics for the grand regime where the tail-generated epitropy can drive the movement of energy. |
| format | Article |
| id | doaj-art-742d39bcd9c040db8f4734f0fc3177f2 |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-742d39bcd9c040db8f4734f0fc3177f22024-12-27T14:25:00ZengMDPI AGEntropy1099-43002024-11-012612103710.3390/e26121037Diffusion and Kinetic Theory on Very Long Time and Large Space ScalesChristopher Essex0Bjarne Andresen1Department of Mathematics, Middlesex College, The University of Western Ontario, London, ON N6A 5B7, CanadaNiels Bohr Institute, University of Copenhagen, Jagtvej 155 A, DK-2200 Copenhagen N, DenmarkThis paper extends the concept of epitropy, as introduced in previous work, to capture the effects of extreme tail behavior arising naturally over very long time and large space scales. Epitropy has some qualities that parallel entropy, although it is not quite the same. Its function is to capture the effects of a probability distribution function (PDF) having only a finite populated domain, which was introduced to eliminate divergent moment integrals. Unlike entropy, it represents hidden properties from the <i>external</i> (not the internal) that influence other regimes. This paper uses kinetic theory methods to show the necessity of epitropy in order to ensure that divergent moment integrals do not diverge. While on laboratory scales, the issues in question are negligible, we arrive at dynamics for the grand regime where the tail-generated epitropy can drive the movement of energy.https://www.mdpi.com/1099-4300/26/12/1037thermodynamicslarge space and time scalesgrand regimeepitropykinetic theory |
| spellingShingle | Christopher Essex Bjarne Andresen Diffusion and Kinetic Theory on Very Long Time and Large Space Scales Entropy thermodynamics large space and time scales grand regime epitropy kinetic theory |
| title | Diffusion and Kinetic Theory on Very Long Time and Large Space Scales |
| title_full | Diffusion and Kinetic Theory on Very Long Time and Large Space Scales |
| title_fullStr | Diffusion and Kinetic Theory on Very Long Time and Large Space Scales |
| title_full_unstemmed | Diffusion and Kinetic Theory on Very Long Time and Large Space Scales |
| title_short | Diffusion and Kinetic Theory on Very Long Time and Large Space Scales |
| title_sort | diffusion and kinetic theory on very long time and large space scales |
| topic | thermodynamics large space and time scales grand regime epitropy kinetic theory |
| url | https://www.mdpi.com/1099-4300/26/12/1037 |
| work_keys_str_mv | AT christopheressex diffusionandkinetictheoryonverylongtimeandlargespacescales AT bjarneandresen diffusionandkinetictheoryonverylongtimeandlargespacescales |