I was just watching a CFA video on the Mathematics of Turbulence. What piqued me was the explanation between risk and uncertainty. Here is my quick take:
In a general equilibrium, risk, as in standard deviation, is a standardised measure of the sensitivity of price to new information given the uncertainty of that information. It is a measurable quantity reflecting the stable physical properties of a given relationship.
Uncertainty is to do with the randomness and independence of each piece of new information, meaning that while you know the average sensitivity and the distribution of price sensitivity points, you never know what part of the distribution is going to hit you at any given point in time.
But, in a non general equilibrium world with residual price dependency, risk and certainty become much more closely correlated, and risk and uncertainty less correlated.
Risk is no longer wholly a standardised measure of price sensitivity, but a measure of the physical properties of the distance to or from equilibrium and those forces moving pricing points away from or to equilibrium.
Under a general equilibrium, for a stable physical dynamic, risk and uncertainty are constant, yet at a non general equilibrium point, risk and uncertainty are varying but nevertheless related to the physical characteristics and dynamics of the underlying equilibrating relationships. In other words, prices and price reactions are ultimately bound by what the equilibrium relationship would otherwise have been.