Theory of Quantitative Analysis of Free Will Manifestations in Complex Systems

This paper proposes a formal framework for moving the discussion of free will from the metaphysical plane to scientific verifiability. We introduce the concept of free will as an emergent property manifested in complex "agent-environment" systems when they reach a critical region in three-dimensional parameter space. This space is defined by axes of: behavioral determinism ($D$), environmental entropy ($H$), and agent informational complexity ($I_A$). We postulate that a free will act ($F_{sv}$) corresponds to a behavioral pattern satisfying the irreducibility criterion—it cannot be adequately modeled as either a deterministic or purely stochastic process, while demonstrating consistency with the agent's internal value system. We propose specific mathematical estimates for model parameters, formulate testable hypotheses, and outline experimental protocols for their verification in cognitive science, neuroscience, and artificial intelligence research.