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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2019 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2019
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210060 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-210060 |
|---|---|
| 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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
A Geometric Approach to the Concept of Extensivity in Thermodynamics |
| spellingShingle |
A Geometric Approach to the Concept of Extensivity in Thermodynamics García-Ariza, M.Á. |
| title_short |
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_sort |
geometric approach to the concept of extensivity in thermodynamics |
| author |
García-Ariza, M.Á. |
| author_facet |
García-Ariza, M.Á. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210060 |
| 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. |
| work_keys_str_mv |
AT garciaarizama ageometricapproachtotheconceptofextensivityinthermodynamics AT garciaarizama geometricapproachtotheconceptofextensivityinthermodynamics |
| first_indexed |
2025-12-07T21:24:14Z |
| last_indexed |
2025-12-07T21:24:14Z |
| _version_ |
1850886224124837888 |