International Encyclopedia of Systems and Cybernetics

Similar rules of energy use that operate at various levels in a system.

Power laws occur when the average frequency of an event of a given size is inversely proportional to some power of its size. For example, small earthquakes are quite frequent, but much less destructive than the strong ones, which in turn are quite less frequent.

Systems near critical states seem governed by such optimization rules (or power laws) which minimize their expenditures of energy.

As a consequence, according to I. RODRIGUEZ ITURBIDE et all (in P. YAM, 1994, p.17): "Rather than emerging from events happening nearby or taking place immmediately before, critical catastrophes may occur because of a global, long term mechanism. Specifically, the systems may be minimizing the amount of energy they expend in maintaining themselves, thereby optimizing the way in which they develop".

The authors created a mathematical model whose statistical properties are exactly the same as those of a drainage network, in which "the length of the stream channels and the distribution of branches, and of the energy at any point, all obey these (power) laws. It seems also possible that in earthquakes models, tectonic plates may be organizing themselves locally so as to minimize stress for the entire system".

The same model could explain how "trees are optimizing their leaf distribution to take advantage of the light they receive".

YAM adds: "The finding raises the question of whether all self-organized critical systems evolve through some global principle of energy minimization". It also poses interesting question marks about the ways of interactions between particles, elements or agents which are not connected in any known functional way. We obviously need not only a model of global action, but also one of local and possibly non-local action in connection with the global one.

This could lead to a clearer interpretation and understanding of holographic order and, generally, of implicate order in BOHM's terms and even possibly make sense of R. SHELDRAKE's morphic fields.

Power laws seem also related to the fractal character of many systems. They could offer interesting insights in relation to social organization and quiet or violent change.

A connection between power laws and so called "small worlds"is also probable; the many frequent small connecting steps among nearby elements are somehow opposed to unfrequent big leaps between distant hubs in a network.

This can be observed for instance as two different ways of propagation in epidemics

Power laws seem also to explain some typical relations in ecosystems (A. FROOD, 2001, P. 30-33)

It could be said that power laws and fractalization are the two faces of the same coin.

This is also obvious in the case of WEIERSTRASS renormalization group transformation

→Self-similarity in the Weirstrass function