Application of Onsager and Prigozhin Variational Principles of Nonequilibrium Thermodynamics to Obtain MHD-Equation Dissipative System in Drift Approximation

  Electromagnetic phenomena in plasma are easier to describe in terms of fields, expressing the electric current through the rotor of the magnetic field. But the approach that ignores the corpuscular aspect of the electric current, as noted by H. Alfven, does not allow describing many processes in space plasma. Indeed, relying on the concept of continuity, it is impossible in the mechanics of continuous media to take into account the fluctuations of hydrodynamic functions formed due to the molecular structure of the medium. At the hydrodynamic level of description, taking into account the structure leads to the Langevin equation. Therefore, to describe processes in a magnetized plasma, it is of certain interest to obtain MHD equations in the drift approximation not
from the Vlasov equations, but based on the principles of Onsager and Prigogine, combined by Gyarmati into one variational principle and obtaining a one-liquid plasma model in the drift approximation. Fluctuations are taken into account by introducing an additional term in the expression for pressure, written in the drift approximation, which is similar to the postulation of the Langevin source for describing Brownian motion. The obtained fluctuating-dissipative system differs from the reversible one-liquid approximation of the two adiabatic invariants of Chu, Goldberger, Low

V.V. Bogdanov. Charpter 6. ISBN 978-1-80355-748-9. Book edited by: Prof. Khalid S. 2022. P. 222 DOI: 10.5772/intechopen.103116