Criteria of self-organization

The aim of this paper is to represent the different criteria of the relative degree of order (or of chaos) in nonequilibrium states of open systems. We shall use as the main criterion the Boltzmann-Gibbs-Shannon entropy, renormalized to a given value of mean effective energy—the effective Hamiltonian function. This criterion is formulated as ‘S-theorem’. ‘S’ stands for ‘Self-organization’ to emphasize that the S-theorem is a criterion of the self-organization. The S-theorem serves also as a tool for checking on the correct choice of the controlling parameters. The comparative analysis of different criteria of self-organization is presented. The connection with the different characteristics of chaotic system (Krylov-Kolmogorov-Sinai (K-entropy) entropy, Lyapunov exponents, Kullback entropy gain, Renyi entropy, nonlinear Kl-entropy, statistical Kst-entropy) are considered.