The Persistent Uncertainty Law: A Complementary Constraint to the Second Law of Thermodynamics

Global uncertainty cannot be eliminated. Local reductions of uncertainty—achieved through interaction, correlation, and thermodynamic processes—produce structured and metastable configurations, but never exhaust the underlying uncertainty. Residual uncertainty persists and continuously perturbs stabilized configurations, ensuring ongoing dynamics and the emergence of new structure. This work formulates the Persistent Uncertainty Law as a structural constraint complementary to the Second Law of Thermodynamics. While the Second Law constrains the direction of physical processes through entropy, the Persistent Uncertainty Law constrains the admissible configurations of physical systems by forbidding complete closure. Together, these constraints imply that no physically realizable system can reach a final, fluctuation-free state. All physical structures are therefore dynamically maintained, metastable, and subject to ongoing perturbation. This paper presents the law in a constraint-level formulation, independent of any specific microscopic model, and establishes its role as a foundational principle governing structure, stability, and dynamical openness.