Geodesic
Entropy in Thermodynamics: from Foliation to Categorization
Communications in Mathematics, Tome 29 (2021) no. 1, pp. 49-66.

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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.
Classification : 80-10, 80A05
Keywords: Entropy; Thermodynamics; Contact structure; Ordering; Posets; Galois connection 
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Kycia, Radosław A. Entropy in Thermodynamics: from Foliation to Categorization. Communications in Mathematics, Tome 29 (2021) no. 1, pp. 49-66. http://geodesic.mathdoc.fr/item/COMIM_2021__29_1_a3/