Synergetics

Abstract

Synergetics is offered as a physical construct for understanding self-organization. It is a mathematical—physical way of studying how collections of subsystems (such as atoms, cells, animals) can produce structures and patterns by self-organization. The construct is applicable to all kinds of matter. The great generality of thermodynamics pertains to thermal equilibrium or, in irreversible thermodynamics, to systems driven only slightly from that equilibrium. When systems are driven very far from equilibrium, however, new things can happen, and the classic concepts of thermodynamics are no longer adequate. Ordered structures can arise out of formerly chaotic states and can be maintained by energy and matter fluxes passing through the system. The laser is used as an example to exhibit the general concepts and principles of these new “instability” states that can possess ever-increasing order.

The concept of “slaving” is fundamental in synergetics. Long-lasting quantities may enslave short-lasting quantities. Symmetry-breaking or selection of bistable state alternatives also may be important in nonequilibrium systems. Because of the slaving principle, there can be an enormous resentative of such higher-ordered enslaving principles. At critical instability points, nonequilibrium systems “test” various configurations or collective notions by fluctuations. These configured dynamic “modes” can act as order parameters and enslave all other modes of the system. This structuring of order parameters can occur within an entire hierarchy of instability points.

There are two possible outcomes of such phenomena: completely chaotic motion that can decay to a structureless state when power is turned off; or, typical of biological systems, structure that is maintained even when metabolic processes stop. Function can be latent in form.

A mathematical schema is provided and applied to a “morphogenetic” example. —The Editor