A Geometric Approach to the Concept of Extensivity in Thermodynamics
This paper presents a rigorous treatment of the concept of extensivity in equilibrium thermodynamics from a geometric point of view. This is achieved by endowing the manifold of equilibrium states of a system with a smooth atlas that is compatible with the pseudogroup of transformations on a vector...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2019 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210060 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A Geometric Approach to the Concept of Extensivity in Thermodynamics / M.Á. García-Ariza // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 25 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862744647155056640 |
|---|---|
| author | García-Ariza, M.Á. |
| author_facet | García-Ariza, M.Á. |
| citation_txt | A Geometric Approach to the Concept of Extensivity in Thermodynamics / M.Á. García-Ariza // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 25 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This paper presents a rigorous treatment of the concept of extensivity in equilibrium thermodynamics from a geometric point of view. This is achieved by endowing the manifold of equilibrium states of a system with a smooth atlas that is compatible with the pseudogroup of transformations on a vector space that preserve the radial vector field. The resulting geometric structure allows for accurate definitions of extensive differential forms and scaling, and the well-known relationship between both is reproduced. This structure is represented by a global vector field that is locally written as a radial one. The submanifolds that are transversal to it are embedded and locally defined by extensive functions.
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| first_indexed | 2025-12-07T21:24:14Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210060 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:14Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | García-Ariza, M.Á. 2025-12-02T09:32:21Z 2019 A Geometric Approach to the Concept of Extensivity in Thermodynamics / M.Á. García-Ariza // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 25 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 80A05; 80A10 arXiv: 1807.00873 https://nasplib.isofts.kiev.ua/handle/123456789/210060 https://doi.org/10.3842/SIGMA.2019.015 This paper presents a rigorous treatment of the concept of extensivity in equilibrium thermodynamics from a geometric point of view. This is achieved by endowing the manifold of equilibrium states of a system with a smooth atlas that is compatible with the pseudogroup of transformations on a vector space that preserve the radial vector field. The resulting geometric structure allows for accurate definitions of extensive differential forms and scaling, and the well-known relationship between both is reproduced. This structure is represented by a global vector field that is locally written as a radial one. The submanifolds that are transversal to it are embedded and locally defined by extensive functions. The author wishes to thank Gerardo F. Torres del Castillo, Merced Montesinos, Hernando Quevedo, and Alessandro Bravetti for their valuable comments regarding this work. The referees are acknowledged for helping to substantially improve this manuscript with their reports. This work was financially supported by VIEP, BUAP. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Geometric Approach to the Concept of Extensivity in Thermodynamics Article published earlier |
| spellingShingle | A Geometric Approach to the Concept of Extensivity in Thermodynamics García-Ariza, M.Á. |
| title | A Geometric Approach to the Concept of Extensivity in Thermodynamics |
| title_full | A Geometric Approach to the Concept of Extensivity in Thermodynamics |
| title_fullStr | A Geometric Approach to the Concept of Extensivity in Thermodynamics |
| title_full_unstemmed | A Geometric Approach to the Concept of Extensivity in Thermodynamics |
| title_short | A Geometric Approach to the Concept of Extensivity in Thermodynamics |
| title_sort | geometric approach to the concept of extensivity in thermodynamics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210060 |
| work_keys_str_mv | AT garciaarizama ageometricapproachtotheconceptofextensivityinthermodynamics AT garciaarizama geometricapproachtotheconceptofextensivityinthermodynamics |