On Higher Order Structures in Thermodynamics
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Publication:6348399
DOI10.3390/E22101147arXiv2009.02077WikidataQ104108546 ScholiaQ104108546MaRDI QIDQ6348399
Mikhail Roop, Valentin V. Lychagin
Publication date: 4 September 2020
Abstract: We present the development of the approach to thermodynamics based on measurement. First of all, we recall that considering classical thermodynamics as a theory of measurement of extensive variables one gets the description of thermodynamic states as Legendrian or Lagrangian manifolds representing the average of measurable quantities and extremal measures. Secondly, the variance of random vectors induces the Riemannian structures on the corresponding manifolds. Computing higher order central moments one drives to the corresponding higher order structures, namely, the cubic and the fourth order forms. The cubic form is responsible for the skewness of the extremal distribution. The condition for it to be zero gives us so-called symmetric processes. The positivity of the fourth order structure gives us an additional requirement to thermodynamic state.
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