Duality - Sealed Variation

Abstract

Self-organization is a phenomenon widely observed in physics, chemistry, and biology. Usually, it is mentioned in the context of far-from-equilibrium of dissipative open systems describing the discharge of entorpy, but the other aspect, formation of self-assembly, is sealed in the total set of stationary solutions of thermodynamically closed systems. This stationary problem is contained in a hierarchy of the mean field of many self-interacting particles, whereby the transmission of free energy is a leading factor. We can observe a unified structure of calculus of variation in these mathematical models, and obtain a guideline of the study from it, especially the total structure of stationary solutions and its roles in dynamics.