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A Geometric Approach to the Concept of Extensivity in Thermodynamics
Symmetry, integrability and geometry: methods and applications, Tome 15 (2019) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: homogeneous functions; extensive variables; equilibrium thermodynamics. 
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     author = {Miguel \'Angel Garc{\'\i}a-Ariza},
     title = {A {Geometric} {Approach} to the {Concept} of {Extensivity} {in~Thermodynamics}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a14/}
}
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Miguel Ángel García-Ariza. A Geometric Approach to the Concept of Extensivity in Thermodynamics. Symmetry, integrability and geometry: methods and applications, Tome 15 (2019). http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a14/

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