Operationalizing the Principle of Dynamical Sensitivity: Response, Coupling, and Cross-Scale Interaction

The first paper introduced the Principle of Dynamical Sensitivity as a conceptual framework suggesting that structures emerging within a shared dynamical physical environment inherit sensitivity to its dynamical properties. The present work aims to operationalize this principle by introducing a simple response-based analytical framework for describing how systems react to the dynamical spectrum of their environment. In the proposed formulation, the environment is treated as a spectrum of dynamical influences, while the system is characterized by a frequency-dependent response function. Within this framework, dynamical sensitivity is expressed through a spectral sensitivity profile, and the realized response of the system is described as the product of environmental dynamics and system susceptibility. An integrated criterion is introduced to distinguish weak background influence from dynamically significant interaction. The proposed formalism does not introduce a new physical interaction. Instead, it provides an analytical language intended to compare dynamical sensitivity across physics, chemistry, and biology, and to clarify how resonance, coupling, and synchronization may be understood as particular manifestations of a broader responsiveness to a shared dynamical environment