Self-organization in non-equilibrium systems—such as Bénard convection, chemical oscillations, and Turing patterns—is characterized by the emergence of ordered structures sustained by energy flow. This work introduces a phenomenological parameter inspired by Energy-Efficiency Theory (EET) to characterize the energetic conditions for the onset of self-organization. We define a non-equilibrium energy ratio ηnoneq=E˙resp/E˙totalηnoneq=E˙resp/E˙total, where E˙respE˙resp is the non-thermal power absorbed from external driving and E˙totalE˙total is the total power input. Both quantities are measurable via calorimetry and power balance. We propose that the onset of self-organization occurs when ηnoneqηnoneq exceeds a system-dependent threshold ηcηc. The framework does not derive ηcηc from first principles; instead, it provides testable predictions: (1) For Bénard convection, ηcηc correlates with the fluid's constraint barrier EbEb and relaxation rate ββ; (2) The pattern wavelength above onset scales with ηnoneq−ηcηnoneq−ηc; (3) In chemical oscillators, the oscillation period scales with 1/(ηnoneq−ηc)1/(ηnoneq−ηc). These predictions are stated with explicit experimental protocols, statistical power analysis, and falsification criteria. The framework is explicitly limited to systems where a single order parameter characterizes the instability and is intended as a complementary phenomenological tool, not a replacement for classical non-equilibrium thermodynamics.
Hongpu Yang (Thu,) studied this question.