... "ergodic" would seem to pertain to systems that are predictable or states that are repeatable over time, irrespective of the original state.

I might respectively point out that (a) nothing is irrespective of it's original state. And (b) most all systems are, to an extent, predictable. The very term "system" implies a certain "order" that functions.

Let's face it fellows, Noah Webster's first rule of definitions applies here, i.e. No definition of a word should be more oblique than the word itself.

So...Ergodic:
adjective: positive recurrent aperiodic state of stochastic systems; tending in probability to a limiting form that is independent of the initial conditions.
...as such, is very likely contrived scientific jive and is, therefore, gobbledygook.

Unless, of course, they meant something akin to "stabilization".