Nonergodic complexity management

Linear response theory, the backbone of nonequilibrium statistical physics, has recently been extended to explain how and why nonergodic renewal processes are insensitive to simple perturbations, such as in habituation. It was established that a permanent correlation results between an external stimulus and the response of a complex system generating nonergodic renewal processes, when the stimulus is a similar nonergodic process. This is the principle of complexity management, whose proof relies on ensemble distribution functions. Herein we extend the proof to the nonergodic 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.