Fragmented physical statistics and self-ordering processes in complex systems

This paper is a continuation of two previous articles devoted to an attempt to estimate the contribution of the spatial disorder of molecular systems in their particular states (critical liquid-vapor transition points). Using fractal modeling for dynamic stochastic systems made it possible to single out two statistical multipliers, GN and FZ, based on the difference between the ways of particle interaction (GN) and considering the system’s motion as such in the phase space (FZ). These multipliers form the basis of physical statistics based on a deep understanding of the types of interactions and their consequences. In addition, it is shown that the physical statistics multipliers GN and FZ have different content when applied to systems with a quantum nature of interactions or other phase space elements. As a result, the idea arose about the possibility of forming fragmented physical statistics, which would differentiate both the interactions between the particles of systems and individual elements of the phase space, aiming to highlight the general patterns inherent in their particular states. The present paper is devoted to forming such fragmented physical statistics and the individual results of its application. The main asset of the proposed method for considering statistical problems is the rethinking of the phase space of dynamic stochastic systems, in which one can single out (as a separate element of the phase space) the space of solid angles of orientation of momenta (or wave vectors) of system particles. Accordingly, an additional component of the entropy of systems in certain states appears – the orientational component of entropy. The only reason for the appearance of an additional orientation component of entropy in all cases is the mechanism of mono energization of the particle spectrum, the physical nature of which can be very diverse. However, the statistical result is always the same: a sharp increase in the orientation component of entropy with the emergence of a direction distinguished in the system. The selected direction can be inherent in the system or imposed on it by external influence – then we will call such ordering in systems generation. If the selected direction arises spontaneously, then we will call it self-ordering process. Often such a self-ordering process is also stochastic, such as turbulence. The paper’s conclusion is as follows: the increase in entropy in systems occurs not only when they approach the state of equilibrium but also when self-ordering processes appear in them.