State-Space Curvatures and Self-Organizing Criticalities

Self-organizing criticalities are a much studied notion, within disciplines ranging from ecosystems/living systems to economic systems and markets. But there is still no consensus or general framework for explaining the ’spontaneous’ emergence of this kind of ’orderly’ behavior. This paper generalizes the second law of thermodynamics to dynamic state-spaces with increasing dimensionality and introduces the notion of spate-space curvature, in order to provide such a framework.