2026PaperV6
The paper proposes a unified theoretical framework for analyzing complex adaptive systems—ranging from social and economic systems to biological neural networks and large language model architectures—by focusing on two agent‑level variables: power (Ai), which quantifies an agent’s influence on collective outcomes, and response functions (Bi), which capture how agents react to observations. Starting from a feedback‑loop model linking external forces, agent actions, and observations, the author derives macroscopic system properties such as total power (W), useful energy (D = Σ Ai Bi), entropy (S = (W‑D)/W), synchronization, fragility, and a novel third dimension, mobility (inverse of viscosity, V = Σ|B_i|). A utility function u(W)=W^g, parameterized by a risk‑appetite coefficient g (linked to relative risk aversion), is introduced to formalize the trade‑off between growth, stability, and adaptability. By maximizing the expected utility (or a simplified objective G that combines growth, variance, and mobility), the analysis yields conditions for an “optimal order” where concentration of power and synchronization of responses are balanced against systemic risk and mobility. The paper argues that order, entropy, information, and useful energy are task‑dependent, system‑relative concepts, and demonstrates how the framework can be applied to AI multi‑agent architectures, neural systems, financial markets, public opinion dynamics, and macro‑economic policy. The work integrates and extends ideas from mean‑field games, stochastic games, dynamical systems, agent‑based modeling, and control theory, offering a common language for designing and diagnosing complex systems.
Topics
Feedback Loop Model: Power (A_i) and Response Functions (B_i) as Fundamental Agent Variables
Introduces the core mathematical structure where each agent’s influence (A_i) and its reaction coefficient (B_i) drive the evolution of observations through a feedback loop with external forces.
Deriving Macroscopic System Quantities from Micro‑Level Parameters
Shows how total power W, useful energy D, entropy S, and other aggregate measures emerge analytically from the distributions of A_i and B_i.
Optimal Order: Balancing Growth, Stability, and Mobility
Formulates the trade‑off problem, introduces objective G that combines growth, variance, and mobility, and identifies conditions where concentration and synchronization are neither too high nor too low.
Mobility and Viscosity: A Third Dimension of System Quality
Defines mobility as the inverse of viscosity (V = Σ|B_i|), argues that high productivity without mobility leads to rigidity, and incorporates mobility into the optimization objective.
Task‑Dependent Redefinition of Order, Entropy, Information, and Useful Energy
Argues that these concepts are relative to system goals and receivers, distinguishing information entropy from system entropy and linking useful energy to task‑specific order.
Cross‑Domain Applications: AI, Neural Systems, Markets, and Public Opinion
Maps the abstract framework onto concrete domains—LLM multi‑agent architectures, biological neural networks, financial markets, and social media—illustrating how power‑response distributions explain observed phenomena.