Simplexity

Summary of “Dynamical Theory of Complex Systems with Two-Way Micro–Macro Causation”

From the Perspective of Complexity and Cybernetics

Overview

The paper by Harte et al. (2024) introduces a novel dynamical framework, Dynamic Maxent across Entwined Scales (DyMES), to address the challenges of modeling complex systems where bidirectional causation exists between micro- and macro-level dynamics. In traditional complexity science and cybernetics, systems are often studied through either Bottom-Up mechanistic modeling (micro-level dynamics driving macro-level outcomes) or Top-Down statistical inference (macro-level constraints influencing micro-level behavior). DyMES integrates both approaches, offering a hybrid system that incorporates feedback across scales to model and predict the behavior of systems with cross-scale dependencies. The theory leverages information entropy (Maxent) and mechanistic transition functions to describe and simulate dynamic, non-equilibrium systems.

Key Contributions to Complexity Science

  1. Bidirectional Micro-Macro Causation and Scale Entwinement
    • Complex systems often exhibit two-way causation:
      • Micro to Macro (Bottom-Up): Micro-variables aggregate into macro-level state variables.
      • Macro to Micro (Top-Down): Macro-level state variables influence microscale dynamics.
    • Examples include:
      • Epidemiology: Disease incidence at the population level (macro) influences individual behavior (micro).
      • Economics: Macroeconomic indicators (e.g., GDP) shape individual financial decisions.
      • Ecology: Population size and species diversity (macro) impact individual growth or reproduction rates.
    • DyMES formalizes this “entwinement” by explicitly modeling feedback loops across hierarchical levels, which is critical for understanding system resilience, adaptability, and emergent behavior.
  2. Dynamic Maxent Framework
    • The framework merges Shannon entropy maximization (Maxent) with dynamic constraints imposed by time-evolving macro-variables.
    • Traditional Maxent assumes equilibrium, but DyMES extends it to non-equilibrium systems by dynamically updating constraints (state variables and their time derivatives).
    • Key innovation: Lagrange multipliers evolve dynamically, enabling rapid computation of state-variable trajectories even in high-dimensional systems.
  3. Redefining Feedback in Complex Systems
    • In cybernetics, feedback is central to understanding system regulation and stability. DyMES highlights a distinct form of feedback:
      • Cross-scale feedback: Unlike traditional feedback (e.g., between subsystems at the same level), DyMES models interactions between hierarchical levels (micro and macro).
      • This introduces novel dynamics, such as:
        • Hysteresis: Delayed recovery or overshooting when parameters return to initial values.
        • Reddened spectra: Enhanced low-frequency variability in response to stochastic perturbations.
  4. Dynamic Predictive Power
    • DyMES predicts both:
      • Macro-variable trajectories (e.g., population size, economic output).
      • Micro-variable distributions (e.g., income inequality, species abundance).
    • This enables better modeling of non-steady-state systems, where traditional methods (e.g., static Maxent or mechanistic models) fail.

Cybernetics Perspective

From a cybernetics standpoint, DyMES provides a framework for understanding and managing adaptive systems through feedback and information flow at multiple scales. Key cybernetic principles reflected in DyMES include:

  1. Information as a Control Mechanism
    • DyMES relies on Shannon entropy to encode information about system states. By maximizing entropy, it ensures a “least-biased” distribution of micro-variables consistent with macro-level constraints.
    • Feedback is regulated by how macro-level information updates micro-level transition functions, effectively creating a cybernetic loop where information governs system behavior.
  2. Self-Organization and Emergence
    • The interplay of micro- and macro-level feedback results in emergent behaviors, such as steady-state distributions, oscillations, or hysteresis.
    • DyMES captures how local interactions (micro) combine with global constraints (macro) to drive system-level organization.
  3. Resilience and Perturbation Response
    • The framework models how systems respond to external disturbances:
      • Slowed recovery times due to scale entwinement (top-down influences).
      • Nonlinear behaviors and hysteresis caused by delayed feedback loops.
    • These insights align with cybernetics’ focus on system adaptability and robustness under changing conditions.

Applications in Complex Systems

DyMES is applied to various domains, demonstrating its interdisciplinary scope and relevance to both complexity and cybernetics:

  1. Chemical Thermodynamics
    • Models the non-equilibrium distribution of molecular kinetic energies during chemical reactions, accounting for feedback between molecular-scale dynamics and system-level energy changes.
  2. Epidemiology
    • Predicts the spread of diseases in social clusters where individual behavior adapts based on macro-level disease prevalence (e.g., public health warnings influencing personal actions).
  3. Economics
    • Links income inequality (micro) to national economic growth (macro), showing how policies can influence interdependent patterns of wealth distribution and GDP growth.
  4. Ecology
    • Explores population dynamics in ecosystems, emphasizing how species-level interactions (micro) and community-level properties (macro) co-determine outcomes like biodiversity and resilience to perturbations.

Novel Dynamics Predicted by DyMES

  1. Hysteresis
    • Macro-scale variables may not return to pre-perturbation states even after external conditions are restored, indicating memory-like behavior in complex systems.
  2. Reddened Time Series Spectra
    • DyMES predicts enhanced low-frequency variability in response to white noise, reflecting slower recovery rates and long-term system memory.
  3. Multiple Steady States
    • Systems modeled by DyMES may exhibit distinct steady states based on the interaction of micro- and macro-level dynamics, including states with non-zero Lagrange multipliers.

Implications for Complexity and Cybernetics

  1. Unified Framework for Multi-Scale Modeling
    • DyMES bridges the gap between Bottom-Up (mechanistic) and Top-Down (statistical) approaches by integrating information-theoretic inference with dynamic feedback mechanisms.
    • This offers a powerful tool for modeling systems that cannot be fully understood by micro-level or macro-level analysis alone.
  2. Cross-Disciplinary Applicability
    • By generalizing concepts like entropy, feedback, and transition functions, DyMES provides a versatile framework for applications in physical, biological, social, and economic systems.
  3. Insights into Resilience and Adaptation
    • The framework’s ability to predict hysteresis, slow recovery, and emergent variability aligns with cybernetics’ emphasis on understanding and managing systems under stress or perturbation.
  4. Tool for Policy and Decision-Making
    • DyMES could inform strategies for managing complex systems, such as designing economic policies to reduce inequality or ecological interventions to enhance biodiversity and resilience.

Conclusion

From a complexity and cybernetics perspective, DyMES represents a significant step forward in modeling and understanding systems with entwined micro-macro dynamics. By explicitly incorporating bidirectional feedback, it provides a robust framework for studying the emergent, adaptive, and non-equilibrium behaviors that are hallmarks of complex systems. Its applications to ecology, economics, epidemiology, and thermodynamics exemplify its interdisciplinary relevance, making it a valuable tool for both theoretical exploration and practical problem-solving in cybernetics and beyond.

References

https://www.santafe.edu/news-center/news/hybrid-theory-offers-new-way-to-model-disturbed-complex-systems