Entropy in thermodynamics can be presented through contact geometry, Lieb-Yngvason ordering axioms, and poset categories, with a Galois connection, the Landauer connection, as the categorical bridge.
tom Dieck, Transformation Groups and Representation Theory, Lecture Notes in Mathematics
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Entropy in Themodynamics: from Foliation to Categorization
Entropy in thermodynamics can be presented through contact geometry, Lieb-Yngvason ordering axioms, and poset categories, with a Galois connection, the Landauer connection, as the categorical bridge.