Abstract
It is shown how the methods of Riemannian and Finslerian geometry may be used in thermodynamics of equilibrium and nonequilibrium states. In both cases the Riemannian structure on the spaces of thermodynamic parameters is defined by means of the relative information (entropy). Thermodynamic meaning of the Riemannian scalar curvature is then interpreted in terms of stability of the considered systems. For nonequilibrium systems the time derivative of the relative information leads to the Finslerian structure. It is shown how a homogenization procedure of Rund leads to the Finslerian metric of the Kropina type. Three types of the Finslerian curvature tensors connected with the Cartan connection are considered for two-dimensional spaces. In particular, the so-called horizontal curvature is considered in detail. It turns out that in thermodynamic spaces Cartan connection coincides with the Berwald connection. Thermodynamic meaning of the Finslerian scalar curvatures is not clear since they vanish for two-dimensional spaces.
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Work supported by The State Committee for Scientific Research, project KBN 2 0412 91 01.
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Mrugala, R. Riemannian and Finslerian geometry in thermodynamics. Open Syst Inf Dyn 1, 379–396 (1992). https://doi.org/10.1007/BF02228846
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DOI: https://doi.org/10.1007/BF02228846