S-theorem

Abstract

The question: "What is self-organization?" is very interesting and very difficult. It is possible to find many examples of self-organizing systems, many examples of equations for the description of different processes of self-organization, but it is not easy to propose the most simple and most general quantitative criterion of self-organization [1-3]. In the papers [4-13] the following statement (called S-theorem in [4]) for some different systems was formulated: If, as the value of the control parameter is increased and the system recedes from the "equilibrium" state, the Boltzmann-Gibbs entropy renormalized to a given value of mean "energy" (effective Hamiltonian) decreases, then the process of self-organization is under way. Here we want to give the general proof of the S-theorem. © 1987 Springer-Verlag.