Invariance Properties of the Entropy Production, and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems
This study examines the invariance properties of the thermodynamic entropy production in its global (integral), local (differential), bilinear, and macroscopic formulations, including dimensional scaling, invariance to fixed displacements, rotations or reflections of the coordinates, time antisymmet...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/11/1515 |
| _version_ | 1797510382631256064 |
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| author | Robert K. Niven |
| author_facet | Robert K. Niven |
| author_sort | Robert K. Niven |
| collection | DOAJ |
| description | This study examines the invariance properties of the thermodynamic entropy production in its global (integral), local (differential), bilinear, and macroscopic formulations, including dimensional scaling, invariance to fixed displacements, rotations or reflections of the coordinates, time antisymmetry, Galilean invariance, and Lie point symmetry. The Lie invariance is shown to be the most general, encompassing the other invariances. In a shear-flow system involving fluid flow relative to a solid boundary at steady state, the Galilean invariance property is then shown to preference a unique pair of inertial frames of reference—here termed an <i>entropic pair</i>—respectively moving with the solid or the mean fluid flow. This challenges the Newtonian viewpoint that all inertial frames of reference are equivalent. Furthermore, the existence of a shear flow subsystem with an entropic pair different to that of the surrounding system, or a subsystem with one or more changing entropic pair(s), requires a source of negentropy—a power source scaled by an absolute temperature—to drive the subsystem. Through the analysis of different shear flow subsystems, we present a series of governing principles to describe their entropic pairing properties and sources of negentropy. These are unaffected by Galilean transformations, and so can be understood to “lie above” the Galilean inertial framework of Newtonian mechanics. The analyses provide a new perspective into the field of <i>entropic mechanics</i>, the study of the relative motions of objects with friction. |
| first_indexed | 2024-03-10T05:31:40Z |
| format | Article |
| id | doaj.art-9c9c1fd2a8334d15bbd9d226a47b007a |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T05:31:40Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-9c9c1fd2a8334d15bbd9d226a47b007a2023-11-22T23:16:06ZengMDPI AGEntropy1099-43002021-11-012311151510.3390/e23111515Invariance Properties of the Entropy Production, and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow SystemsRobert K. Niven0School of Engineering and Information Technology, The University of New South Wales, Canberra, ACT 2600, AustraliaThis study examines the invariance properties of the thermodynamic entropy production in its global (integral), local (differential), bilinear, and macroscopic formulations, including dimensional scaling, invariance to fixed displacements, rotations or reflections of the coordinates, time antisymmetry, Galilean invariance, and Lie point symmetry. The Lie invariance is shown to be the most general, encompassing the other invariances. In a shear-flow system involving fluid flow relative to a solid boundary at steady state, the Galilean invariance property is then shown to preference a unique pair of inertial frames of reference—here termed an <i>entropic pair</i>—respectively moving with the solid or the mean fluid flow. This challenges the Newtonian viewpoint that all inertial frames of reference are equivalent. Furthermore, the existence of a shear flow subsystem with an entropic pair different to that of the surrounding system, or a subsystem with one or more changing entropic pair(s), requires a source of negentropy—a power source scaled by an absolute temperature—to drive the subsystem. Through the analysis of different shear flow subsystems, we present a series of governing principles to describe their entropic pairing properties and sources of negentropy. These are unaffected by Galilean transformations, and so can be understood to “lie above” the Galilean inertial framework of Newtonian mechanics. The analyses provide a new perspective into the field of <i>entropic mechanics</i>, the study of the relative motions of objects with friction.https://www.mdpi.com/1099-4300/23/11/1515entropy productioninvariance propertiesLie symmetriesinertial frames of referencenegentropyshear flow systems |
| spellingShingle | Robert K. Niven Invariance Properties of the Entropy Production, and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems Entropy entropy production invariance properties Lie symmetries inertial frames of reference negentropy shear flow systems |
| title | Invariance Properties of the Entropy Production, and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems |
| title_full | Invariance Properties of the Entropy Production, and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems |
| title_fullStr | Invariance Properties of the Entropy Production, and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems |
| title_full_unstemmed | Invariance Properties of the Entropy Production, and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems |
| title_short | Invariance Properties of the Entropy Production, and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems |
| title_sort | invariance properties of the entropy production and the entropic pairing of inertial frames of reference by shear flow systems |
| topic | entropy production invariance properties Lie symmetries inertial frames of reference negentropy shear flow systems |
| url | https://www.mdpi.com/1099-4300/23/11/1515 |
| work_keys_str_mv | AT robertkniven invariancepropertiesoftheentropyproductionandtheentropicpairingofinertialframesofreferencebyshearflowsystems |