Problems in the statistical theory of open systems: Criteria for the relative degree of order in self-organization processes

The aim of this paper is to examine two problems in the statistical theory of open systems, namely, (1) the connection between statistical and dynamic descriptions of motion in open systems, and the constructive positive role of dynamic instability in atomic motion as a basis for kinetic equations and (2) the different criteria for the relative degree of order in nonequilibrium states of open systems, namely, K-entropy, the Lyapunov function, and the Boltzmann–Gibbs–Shannon entropy renormalized to given mean effective energy (S-theorem). It is shown that the S-theorem can be used to determine the relative degree of order from experimental data on empirical realizations of leading characteristics for different values of control parameters.