Caratheodory: Thermodynamics and Topology

  • Gérard A. MauginEmail author
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 214)


In 1909 there appeared a truly unidentified object in the landscape of thermodynamics. It was an axiomatic formulation of the first and second laws of thermodynamics with geometric and analytic arguments by the mathematician Constantin Caratheodory. This practically ignored the well known experimental factual bases (with heat engines) posed by Carnot and Kelvin, to the benefit of a powerful exploitation of Pfaffian differential forms. This is very convincing to mathematically oriented minds as it introduces the notions of entropy and thermodynamic in a purely mathematical framework, the inverse of temperature playing the role of integrating factor. The present essay analyses the contribution of Caratheodory, its reception by his contemporaries, and the influence it had on some specialists of continuum thermo-mechanics in the second half of the twentieth century.


Thermodynamics First law Second law Adiabatic evolution Inaccessibility of states Entropy Thermodynamic temperature 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institut Jean Le Rond d’AlembertUniversité Pierre et Marie CurieParis Cedex 05France

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