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 on 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: a geometrodynamics of entropy.

The maximization of entropy S within a closed system is accepted as an inevitability (as the second law of thermodynamics) by statistical inference alone. The Maximum Entropy Production Principle (MEPP) states that not only S maximizes, but $\dot{S}$ as well: a system will dissipate as fast as possible. There is still no consensus on the general validity of this MEPP, even though it shows remarkable explanatory power (both qualitatively and quantitatively), and has been empirically demonstrated for many domains. In this theoretical paper I provide a generalization of entropy gradients, to show that the MEPP actually follows from the same statistical inference, as that of the 2nd law of thermodynamics. For this generalization I only use the concepts of super-statespaces and microstate-density. These concepts also allow for the abstraction of 'Self Organizing Criticality' to a bifurcating local difference in this density, and allow for a generalization of the fundamentally unresolved concepts of 'chaos' and 'order'.