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arXiv · 1807.00873

A Geometric Approach to the Concept of Extensivity in Thermodynamics

Miguel Ángel García-Ariza
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Abstract

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.

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Miguel Ángel García-Ariza. 2018-07-02. A Geometric Approach to the Concept of Extensivity in Thermodynamics. https://doi.org/10.3842/sigma.2019.015

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