The Trajectory Break Principle (TBP) establishes a universal limit on controllability in classical, stochastic, and quantum systems. Finite control capacity and finite relaxation time inevitably induce control‑driven trajectory singularities. By identifying two fundamental constants, Kmin and Kmax, TBP defines a universal control zone that constrains all physically realizable trajectories. The principle unifies concepts from dynamical systems, information theory, and quantum mechanics, offering a quantitative framework for predicting when trajectories become unstable or uncontrollable. TBP provides a general, experimentally testable boundary for the applicability of control in physical systems.
Marcel Welsch (Thu,) studied this question.