The approach to the analysis of the dynamic of non-equilibrium open systems and irreversibility

The approach to the analysis of the dynamic of non-equilibrium open systems within the framework of the laws of classical mechanics on the example of a hard-disks is offered. This approach was based on Hamilton and Liouville generalized equations which was deduced for the subsystems of the nonequilibrium system. With the help of generalized Liouville equation it was obtained that two types of dynamics are possible: reversible and irreversible. The connection between the dynamical parameter -generalized field of forces, and entropy is established. The estimation of characteristic time of establishment of equilibrium in the thermodynamic limit is realized. It is shown how from the condition of irreversibility of a hard-disk system, the condition of irreversibility for the rarefied system of potentially interacting particles follows. The explanation of the mechanism of irreversibility is submitted. Introduction. In connection with a modern physics, the Newton’s equation is a background of dynamical picture of the world. It is caused by the fact that all four known fundamental interactions of elementary particles are potential. Potentiality of forces causes reversibility of the Newton equation in time. Hence, dynamics of all natural systems consisting of elementary particles should be reversible. But irreversibility is a basis of evolution. In fundamental physics irreversibility determines the contents of the second law of thermodynamics. According to this law there is function S named entropy, which can grow for isolated systems only, achieving a maximum in an equilibrium state. Thus, the fundamental physics includes areas contradicting each other: reversible classical mechanics and irreversible thermodynamics. So, the rigorous substantiation of the second law of thermodynamics within the framework of the classical mechanics laws is one of the primary tasks of modern physics. This problem keenly reveals difficulties and limits of capability resources of classical methods of physics. Despite of numerous attempts, this problem does not have satisfactory solution up to date. Thus, the question how one can describe