  Linear response theory, the backbone of non-equilibrium statistical physics,
has recently been extended to explain how and why non-ergodic renewal processes
are insensitive to simple perturbations, such as in habituation. It was
established that a permanent correlation resulted between an external stimulus
and the response of a complex system generating non-ergodic renewal processes,
when the stimulus is a similar non-ergodic process. This is the principle of
complexity management, whose proof relies on ensemble distribution functions.
Herein we extend the proof to the non-ergodic case using time averages and a
single time series, hence making it usable in real life situations where
ensemble averages cannot be performed because of the very nature of the complex
systems being studied.
