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Fluid dynamics and thermodynamics as a unified field theory

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Abstract

We study the problem of consistency of equations of continuum dynamics (using the Euler equations and the continuity equation as examples) and thermodynamic equations of state (for the specific free energy, entropy, and volume). We propose a variant of the Hamiltonian formulation of a model that combines the fluid dynamics of a potential flow of a compressible fluid or gas and local equilibrium thermodynamics into a unified field theory. Thermodynamic equations of state appear in this model as second-class constraint equations. As a consistency condition, there arises another second-class constraint requiring that the product of density and temperature should be independent of time. The model provides an in-principle possibility of finding the time dependence of the specific entropy of the arising dynamical system.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    V. P. Pavlov

  2. Center for Global Issues, Institute for International Studies, MGIMO University, pr. Vernadskogo 76, Moscow, 119454, Russia

    V. M. Sergeev

Authors
  1. V. P. Pavlov
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  2. V. M. Sergeev
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Correspondence to V. P. Pavlov.

Additional information

Original Russian Text © V.P. Pavlov, V.M. Sergeev, 2016, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Vol. 294, pp. 237–247.

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Pavlov, V.P., Sergeev, V.M. Fluid dynamics and thermodynamics as a unified field theory. Proc. Steklov Inst. Math. 294, 222–232 (2016). https://doi.org/10.1134/S0081543816060146

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