July 31, 2025

Three Fundamental Laws of Response and the Universal Set of Physically Constrained Response Functions

Key Points

MAIN FINDING: The study identifies three fundamental laws that govern response behaviors across various systems.
KEY EVIDENCE: Analysis of 35 canonical response equations demonstrates a universal structure in responses.
APPROACH: Researchers normalized classical response functions to explore thermodynamic and informational constraints.
SIGNIFICANCE: This work advances understanding of how different fields can be connected through a common framework of response.

Abstract

Across all scales of natural and artificial systems, response to stimuli exhibits a consistent structure: saturating growth, delayed onset, and diminishing gain. We propose that these empirical features derive from three fundamental constraints:(1) thermodynamic saturation,(2) information delay,(3) control stability.We formalize these into a set of admissible response functions, bounded by energy, latency, and dynamic stability. This response set, expressed in normalized rational forms, encompasses classical functions observed in biology, physics, neuroscience, and social systems. By normalizing 35 canonical response equations, we demonstrate that these laws form a universal grammar of response.

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Cite This Study

刘加政 (Thu,) studied this question.

synapsesocial.com/papers/689a0c5fe6551bb0af8cf5b8 https://doi.org/https://doi.org/10.31234/osf.io/ma67k_v1