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Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 26, No. 2, pp. 377-382 (2010)
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Finsler structure in thermodynamics and statistical mechanics

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Takayoshi Ootsuka

Ochanomizu University

**Abstract:** We consider the Finsler structure and contact structure in variational principle of equilibrium thermodynamic theory. Einstein's statistical thermodynamic theory was proposed as a statistical mechanics using macroscopic thermodynamic variables as stochastic variables. We generalise Einstein's statistical theory from Finsler geometrical viewpoint, and operating inverse process of variation, path integration, we propose a new statistical theory. Einstein's theory becomes the WKB approximation of our new theory.

**Classification (MSC2000):** 53B40

**Full text of the article:**

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