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Nonergodic complexity management.

Nicola Piccinini1, David Lambert1, Bruce J West2

  • 1Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, Texas 76203-1427, USA.

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Summary
This summary is machine-generated.

Complex systems with nonergodic renewal processes exhibit resilience to external stimuli. This study proves that such systems maintain a permanent correlation with similar nonergodic stimuli, a principle applicable to real-world scenarios.

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Area of Science:

  • Statistical Physics
  • Complex Systems Theory
  • Nonlinear Dynamics

Background:

  • Linear response theory is fundamental to nonequilibrium statistical physics.
  • Nonergodic renewal processes demonstrate insensitivity to perturbations, observed in phenomena like habituation.
  • Previous work established complexity management via ensemble distribution functions for nonergodic processes.

Purpose of the Study:

  • To extend the proof of the complexity management principle to nonergodic cases.
  • To adapt the principle for practical applications using time-series data.
  • To explain the inherent resilience of complex systems to specific types of stimuli.

Main Methods:

  • Extension of linear response theory to nonergodic systems.
  • Utilizing time averages and single time series analysis.
  • Mathematical proof based on statistical physics principles.

Main Results:

  • A permanent correlation is established between a complex system's response and a similar nonergodic external stimulus.
  • The complexity management principle is proven applicable using time averages, not just ensemble averages.
  • The findings validate the robustness of nonergodic renewal processes.

Conclusions:

  • The complexity management principle is now demonstrable with single time series data, enhancing its real-world applicability.
  • This research provides a theoretical framework for understanding habituation and similar phenomena in complex systems.
  • The study bridges theoretical statistical physics with practical analysis of complex system behavior.