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Are the geometries of the first and second laws of thermodynamics compatible?

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  • First and second laws of thermodynamics are naturally associated, respectively, to contact and Hessian geometries. In this paper we seek for a unique geometric setting that might account for both thermodynamic laws. Using Riemannian metrics that are compatible with the contact structure, we prove that the Hessian manifold of thermodynamic states cannot isometrically be embedded as Legendre submanifold of a contact manifold. Well known fibrations suggest the nature of the obstruction for such embedding.
    Mathematics Subject Classification: Primary: 53D10, 53Z05; Secondary: 80A05.


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