Dynamical theory of complex systems with two-way micro-macro causation.

Area of Science:

• Multidisciplinary approach to complex systems
• Theoretical physics and applied sciences

Background:

• Complex systems exhibit microscale dynamics dependent on macroscale variables.
• Scale-entwined systems require integrated modeling approaches, as neither top-down nor bottom-up methods suffice alone.

Purpose of the Study:

• To develop and explore a dynamic theory integrating top-down information-theoretic inference with bottom-up mechanisms.
• To predict the behavior of scale-entwined systems under perturbation.

Main Methods:

• Developed a dynamic theory combining information-theoretic inference and state-variable-dependent mechanisms.
• Utilized analytic expressions for Lagrange multipliers from Maxent solutions for efficient computation.
• Applied the theory to diverse systems including chemical thermodynamics, epidemiology, economics, and ecology.

Main Results:

• The theory predicts nonstationary probability distributions and relates macrovariable trajectories to these distributions.
• Demonstrated scale entwinement leads to slowed recovery, reddened spectra, and hysteresis in a low-dimension example.
• Enabled rapid calculation of state variable trajectories in high-dimensional systems.

Conclusions:

• The integrated theory offers a powerful framework for understanding and predicting the behavior of scale-entwined complex systems.
• Highlights the potential for broad applicability across natural and social sciences.
• Provides insights into phenomena like hysteresis and altered system dynamics due to scale entwinement.