Coherence Complexity (Ck): A Structural Measure of Integration Effort in Adaptive State Spaces

Abstract Adaptive systems are constantly exposed to perturbations that must be integrated into their internal state structure. Maintaining stability therefore requires the ability to incorporate new states while preserving internal coherence. In this work, Coherence Complexity (Cₖ) is introduced as a structural measure describing the integration effort required to harmonize a system state relative to a persistent reference structure within the system’s state space. Cₖ is defined through a distance function between system states and a reference integration core and can be formulated within a variational framework. This formulation provides a geometric perspective on adaptive integration processes in dynamic systems. A numerical simulation illustrates the emergence of attractor structures and the gradient-driven evolution of system states within the resulting coherence landscape.