Friday, April 22, 2011

Stochasticity can lead to Stability

While we think of "noise" as a destabilizing force, we actually use noise many times to lead a system to the most stable position. Consider the scenario where you want to get all the items out of a hand bag very quickly; you would hold the bag up-side-down and shake, i.e. add noise. If you just tilt the bag up-side-down, there is a risk that some of the items would get stuck in the bag. Shaking ensures that such temporary "traps" (in mathematical terms, local minima) are avoided. In a sense, this is like stochastic optimization. When all the items are on the floor, they will remain there even if you shake the floor, because that is that is the most stable position.

Perhaps stochasticity in natural systems is a means of "shaking", i.e. a means by which natural systems reach the most stable states and avoid local traps. The most stable state remains relatively stable even at the presence of noise. Consider the situation when all the items from the bag are on the floor -- even shaking the floor would not change the situation significantly. Perhaps this is the nature of the "most stable state" -- it has a wide basin and thus can easily tolerate noise.

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