Entropy in Thermodynamics: from Foliation to Categorization

Entropy in Thermodynamics: from Foliation to Categorization

We overview the notion of entropy in thermodynamics. We start from the smooth case using differential forms on the manifold, which is the natural language for thermodynamics. Then the axiomatic definition of entropy as ordering on a set that is induced by adiabatic processes will be outlined. Finall...

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Main Author: Kycia Radosław A.
Format: Article
Language:English
Published: Sciendo 2021-06-01
Series:Communications in Mathematics
Subjects:
entropy
thermodynamics
contact structure
ordering
posets
galois connection
80a05
80-10
Online Access:https://doi.org/10.2478/cm-2021-0002
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spelling doaj-a3ae3c3cbd84416eaa0ccc5d10422f9f2021-09-06T19:22:06ZengSciendoCommunications in Mathematics2336-12982021-06-01291496610.2478/cm-2021-0002Entropy in Thermodynamics: from Foliation to CategorizationKycia Radosław A.0Masaryk University, Department of Mathematics and Statistics, Kotlářská 267/2, 611 37Brno, The Czech Republic & Cracow University of Technology, Faculty of Materials Engineering and Physics, Warszawska 24, Kraków, 31-155, PolandWe overview the notion of entropy in thermodynamics. We start from the smooth case using differential forms on the manifold, which is the natural language for thermodynamics. Then the axiomatic definition of entropy as ordering on a set that is induced by adiabatic processes will be outlined. Finally, the viewpoint of category theory is provided, which reinterprets the ordering structure as a category of pre-ordered sets.https://doi.org/10.2478/cm-2021-0002entropythermodynamicscontact structureorderingposetsgalois connection80a0580-10
collection DOAJ
language English
format Article
sources DOAJ
author Kycia Radosław A.
spellingShingle Kycia Radosław A.
Entropy in Thermodynamics: from Foliation to Categorization
Communications in Mathematics
entropy
thermodynamics
contact structure
ordering
posets
galois connection
80a05
80-10
author_facet Kycia Radosław A.
author_sort Kycia Radosław A.
title Entropy in Thermodynamics: from Foliation to Categorization
title_short Entropy in Thermodynamics: from Foliation to Categorization
title_full Entropy in Thermodynamics: from Foliation to Categorization
title_fullStr Entropy in Thermodynamics: from Foliation to Categorization
title_full_unstemmed Entropy in Thermodynamics: from Foliation to Categorization
title_sort entropy in thermodynamics: from foliation to categorization
publisher Sciendo
series Communications in Mathematics
issn 2336-1298
publishDate 2021-06-01
description We overview the notion of entropy in thermodynamics. We start from the smooth case using differential forms on the manifold, which is the natural language for thermodynamics. Then the axiomatic definition of entropy as ordering on a set that is induced by adiabatic processes will be outlined. Finally, the viewpoint of category theory is provided, which reinterprets the ordering structure as a category of pre-ordered sets.
topic entropy
thermodynamics
contact structure
ordering
posets
galois connection
80a05
80-10
url https://doi.org/10.2478/cm-2021-0002
work_keys_str_mv AT kyciaradosława entropyinthermodynamicsfromfoliationtocategorization
_version_ 1717772706136457216

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