Finsler-metrizabilities of spray manifolds

Vattamány, Szabolcs (2010) Finsler-metrizabilities of spray manifolds. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 26 (2). pp. 397-413. ISSN 0866-0174

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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.

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