Local Versus Global Minima, Hysteresis, Multiple Meanings

Although the macroscopic behaviour of a system is quite different according to the fact that the states are described by either the global or the local minima of a potential, the actual simulation of the evolution of physical systems shows the unity of mecanisms. The absence of exterior information to compare the different states (what would not be true of e.g. some economic agents) and the existence of fluctuations, make the choice a matter of time scale and temperature. We shall use some concepts of catastrophe theory (although this theory has not been concerned so far with microscopic mecanisms) like the loop of hysteresis, to study some deterministic ways of finding global minima by acting on a parameter of the system in the context of pattern matching (such as multiresolution) and shall then compare for both alternatives (global or local minima) the functional possibilities relative to A.I.