The book provides a systematic presentation of ideas, methods and results of the modern statistical theory of open systems - systems that exchange matter, energy and information with surrounding bodies. Due to this, in them, along with degradation processes, there are also the processes of self-organization, as a result of which more complex and processes of self-organization, as a result of which more complex and more perfect structures emerge. Statistical criteria of self-organization are considered, in particular, the criterion of the "S-theorem". It is based on the comparison of entropy knowledge renormalized to a certain level of average effective energy. The relative degree of orderliness of the states of open systems is analyzed directly from experimental data. The criterion provides a check of the correctness of the choice of parameters governing the evolution processes. The possibility of a unified description of kinetic, hydrodynamic and diffusion processes in passive and active macroscopic systems without involving the traditional perturbation theory is shown. On this basis, a general definition of heat flux is introduced through the entropy gradient. A sequential calculation of kinetic and hydrodynamic fluctuations is carried out. This approach is widely used in the construction of the theory of classical and anomalous Brownian motion in nonlinear media. The developed theory also opens up the possibility of a new treatment of the phenomenon of turbulence and a unified kinetic description of laminar and turbulent motion. The proposed methods are also used for statistical description of quantum macroscopic open systems. It allows to give answers to "eternal questions": Is quantum-mechanical description complete? Are there hidden parameters in quantum theory?
The book has no analogues in the world literature. It is a monographic textbook and is written largely on the basis of original works of the author.