Stability

Why some particular behavior or structure exists? Is it because it is stable? But, how do we see that it is stable? The circular, and hence implausible, explanation would be: Because it exists. However, the answer that elevates our understanding is: Because the behavior or structure recovers quickly after a small perturbation. Hence, the behavior/structure exists because it is insensitive (robust) to perturbations coming from within or out of the system. Stability is the necessary and sufficient condition for the existence of any system’s behavior /structure. They must be insensitive to perturbations in order to exist. State variables capture the behavioral/structural state of systems.

Indeed, there are myriad influences that any multi-component system suffers from. They all perturb it to some degree. Our skin cell structures, for example, at each moment are perturbed by inumerable low energy (mostly microwave, visible light and soft ultraviolet) radiation. Then, naturally, the question arises: Why system’s behavior and structure does not simply dissolve under those influences. Why they do not destroy it? There must be some kind of interaction between the components that form the behavior that is stronger than the perturbations trying to change it. For example, if the bonds forming our cell structures were weak enough (sensitive to light perturbations) we would not exist. Although Earth’s crust trembles (fluctuates) very weakly continuously, the human made buildings are stable. Only large fluctuations/perturbations (e.g. earthquakes) are those which are able to weaken the bonds between the components that stabilize these buildings. The competition of bond forming couplings and perturbations is present in any system we see. They are an important part of the context which generates system’s stability or instability. Indeed, if couplings between the components of the system are larger than the internal or external perturbing forces trying to decouple them, the system is stable and vice versa.

Instability

The same logic holds for the question: Why some behavior /structure does not exist? Why some thing is impossible?  The answer quickly follows: Because it is not stable under the perturbations coming from within or outside of the system and under the extant context.  Any initially imposed behavior/structure will quickly dissolve under the external or internal perturbations if they are strong enough or if the context is such that destabilizes such imposed behavior/structure. For example, under perturbations of sufficiently high energy (say gamma) light particles or high temperatures our cell structures and functions will immediatelly decompose. No system is insensitive to all types or sizes of perturbations. The nature creates and destroys through instabilities and maintains through stability. This is the Hindu god Shiva, the creator and destroyer, at its core. The Nature is inherently metastable.

Some examples, of how perturbations induce instabilities which produce structures out of homogeneous state are Rayleigh-Taylor instability , Plateau-Rayleigh instability , Kelvin-Helmholtz instability (see here too),liquid-solid transitions of supercooled liquids etc.

Multistability

What happens when the system looses its stability? Well, it can disolve to an unstructured stable state or change itself to another stable, more ordered, behavior and structure. This property of systems to be able to have more than one stable state is called multistability.

 Metastability (State transitions/State switches)

A prerequisite of metastability is multistability. The system must be able to be organized in at least two stable states. Metastability is tightly connected with the time-scales of change of system. Under the same context it may stay for a long time in one state and then quickly switch to another relatively long living state and continue to exibit that behavior. If we observe such system for a short time we may wrongly conclude that that very state is the only stable state. But if we wait long enough we will witness a quick change to another relatively short-living state. These switches may be a result of external perturbations or intrinsic fluctuations acting on the systems organized behavior. They can have also a purely dynamic origin. The system obviously is characterized by at least two time scales: the one that is characteristic for the short term dwelling state and the one characteristic for the evolution among many such states. For, example our thoughts or attention may be focused on some topic for some short time but then quickly switch to another one, and then yet to another one. Our purposefull actions switch all the time. In some people social/psychological perturbations may provoke even switch among multiple personalities . Even our Universe with all of its laws may be a mere short-living metastable state with respect to the grand time-scale of cosmic evolution.

 

Robert Hristovski 22.02.2016