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The effect of noncommutativity of the conservation laws on the development of thermodynamical and gas dynamical instability (The method of skew-symmetric differential forms)

L. I. Petrova
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Abstract

In the works by the author it has been shown that the conservation laws for material media (the conservation laws for energy, linear momentum, angular momentum, and mass, that establish a balance between the variation of a physical quantity and the corresponding external action), turn out to be noncommutative. The noncommutativity of the conservation laws that leads to an emergence of internal forces and an appearance of the nonequilibrium is a cause of development of instability in material media (material systems). These results were obtained with the help of the mathematical apparatus of skew-symmetric differential forms. To study the causes of developing instability it is necessary to inspect the evolutionary relation obtained from equations of the balance conservation laws and to analyze the differential form commutator that enters into this relation. In the present work the method of skew-symmetric differential forms has been applied in study of the thermodynamical and gas dynamical systems. It was shown that the principle of thermodynamics follows from two conservation laws, namely, the balance conservation laws for energy and linear momentum. In this case the second principle of thermodynamics, from which the state function (which specifies a state of the thermodynamical system) is obtained, follows from the first principle. A mechanism of development of instability in gas dynamical systems is described and there are explained such processes as emergence of waves, vortices, turbulent pulsations and so on.

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L. I. Petrova. 2003-11-24. The effect of noncommutativity of the conservation laws on the development of thermodynamical and gas dynamical instability (The method of skew-symmetric differential forms). https://arxiv.org/abs/math-ph/0311040

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