Year: 2025
Type: preprint
Abstract: We demonstrate that all saturating response curves observed in physics, chemistry, biology, and social systems-including sigmoid, logistic, Michaelis-Menten, and exponential relaxation curves-can be naturally derived from the fundamental existence of a minimal causal response time τ 0 > 0. By formalizing the system as a causal low-pass filter with nonlinear input constraints, we show mathematically that any attempt at instantaneous response is physically forbidden, leading inevitably to saturation.The framework unifies previously empirical models under a rigorous physical and mathematical principle.
Author: jiazheng liu
Language: English
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
OpenAlex ID: W4413341606