*Application of Onsager and Prigozhin Variational Principles of Nonequilibrium… DOI: http://dx.doi.org/10.5772/intechopen.103116*

impossible in the mechanics of continuous media to take into account the fluctuations of the hydrodynamic functions formed due to the molecular structure of the medium. At this level of description, taking into account the atomic-molecular structure leads to the Langevin equation, in which the parameters of the medium are described by

random sources. These sources are responsible for fluctuations *ρ*,*V* , *T* and being unavoidable properties of the medium, cannot be excluded. Therefore, postulating Langevin sources in hydrodynamics brings the corresponding equations as close as possible to describing the behavior of a real medium.

In turn, the possibility of taking into account the structure of a physically infinitesimal plasma element in this work was achieved, on the one hand, by using the variational methods of Prigogine and Onsager, combined by Gyarmati, and making it possible to obtain a completely self-consistent equation with the accuracy of the chosen drift approximation. On the other hand, this approximation, being singleparticle, initially takes into account the discreteness of the considered ionized medium ("atomic-molecular" structure). In addition, it admits small perturbations within the limits of its accuracy, that is, within the limits of the constancy of the first adiabatic invariant *μ*.


larger than the distance between collisions on fluctuations. For example, in the problem of plasma flow around the solar wind of the Earth's magnetosphere, the characteristic size of the latter is much less than the mean free path corresponding to Coulomb collisions. This, proceeding from rigorous considerations, indicates the inadmissibility of using the hydrodynamic approximation to describe the processes in this problem. However, the experimental data are in good agreement with the results that follow for this problem from the solution of hydrodynamic equations, which indicates the presence of an effective particle scattering mechanism, which leads to a significant decrease in the mean free path in comparison with Coulomb collisions [12].
