Does this perhaps have some relation to Monte Carlo methods where the qualities of the noise (white, pink blue etc) and/or stratification that you use - can strongly affect the qualities of the integral that results? Could be analogous to the local instabilities in the section you quoted?
(reminds me a lot of how information moves around in a reaction-diffusion simulation too)
It seems likely to. In MCMC this is known as the mixing/convergence speed. If one valid transition kernel decreases the mutual information between samples faster than another it mixes faster. Meaning the sampled chain has better statistical properties (effective number of independent samples).
