Unified non-local relativistic theory of transport processes (Q2825436)

Since the beginning of science many researchers tried to find a description of the surrounding reality having theories that are complete and are able to describe as much as possible of the reality. But the history of science shows that this is not easy. In many cases researchers started with simple (e.g., one-dimensional, limited, without memory effects, etc.) models that, at the beginning, were given to describe the easiest cases. Then, the proposed solutions were developed, expanded and generalized. It is a natural process, but sometimes it takes a long time when we have spectacular paradigm shifts or even changes. However, we are expecting that the development of science takes the following way. This process usually leads to paradigms shifts or even changes; however, each such change is not simple and connects with the fact that a lot of work should be done, even if this progress introduces some controversies.NEWLINENEWLINEThe reviewed book starts with a simple but very convincing introduction where the author lists important facts that are key points. This is a very deep and touching discussion about many aspects of science, philosophy and the author's personal believes. We can discuss whether they are necessary, but after the first chapter we have a strong belief that the author has something important to say. The importance of his words is strengthened by very simple examples and calculations, which show the need of deep study of so far existing approaches, assumptions, problem solutions in physics. This is especially well visible when we take into account all the methods related to multiscale and which are based on physical kinetics.NEWLINENEWLINEMultiscale methods are mostly based on a Boltzmann approach, but in fact in these approaches the particle size effects are not taken into account. The author shows in the successive chapters how this is important, especially in transport processes leading to the emergence of new formulas, which are necessary to have a real generalized kinetic description. The theoretical background is introduced in Chapter 1, and the following chapters are developed to many examples leading to new results in hydrodynamics (both classical and relativistic ones -- Chapters 2, 10, 12), plasma physics (Chapters 7 and 8), phase flows (Chapters 3 and 5), quantum electronic plasma and solid state physics (Chapter 5). The author also introduces some theoretical insights into the Chapman-Eskong theory of gasses, Frenkel's theory of liquid structures, high-atom physics and astrophysics. The obtained results may be sometimes questionable and can lead to confusion.NEWLINENEWLINEStarting from the introduction, the book is full of equations and detailed derivations. It is a big challenge not only to write and control such a big number of expressions, but also to ensure that in all of them there aren't any mistakes. On the one hand, this is a very valuable feature of this book -- the reader can find many important and sometimes even unknown derivations, but the huge amount of details, expressions variables, notations immediately raises some doubts (expressed by simple, however, obvious thought): are there no errors? This is not an objection, but a simple and obvious remark. Let's remember that the book is translated from the Russian language and in some places one can even find Russian letters (typos). Example: page 33, after Equation (I.3.63) we have \(A^{\alpha}\) и \(B^{\alpha}\). On page 21 we have К and \(K'\), which are used for the notation of two systems, but on page 23 it is \(K\) and then also \(K'\) (see also Fig. I.3.1). The same is with references to literature published in Russian.NEWLINENEWLINEGenerally speaking, this book is hard for readers lacking experience with advanced physics, but on the other hand the author gives a lot of illustrations, detailed calculations, results of approximations with necessary precision, explanation of used parameters and finally very detailed equations (there are even places in the book where on one page is one equation). The author offers us a monograph about basic and fundamental relations that are the basement of many existing theories and for those who are looking for new and fresh view on existing theories this is a very valuable monograph.