Phase Coherence, Not Spectral Slope, Determines Recovery in Noise-Driven Bistable Systems

Systemic degradation in complex dynamical systems is often modeled as an in-evitable thermodynamic slide toward equilibrium. However, we present evidence that this decay is fundamentally a noise-accumulation problem governed by spectral properties. Using novel pink noise generation methods, we demonstrate that structural coherence relies on the balance between “constructive entropy” (pink/1fnoise) and “destructive entropy” (Gaussian/white noise). We introduce the Pink-to-White Noise Ratio (PWNR) as a quantitative metric of systemic integrity and show through computational modeling that when PWNR exceeds a critical threshold, systems undergo a phase transition from entropic decay to structural rejuvenation. Our results suggest that “aging” in complex systems is not a fixed temporal vector but a reversible accumulation of spectral incoherence, with profound implications for control theory, network resilience, and non-equilibrium thermodynamics. Systemic degradation in complex dynamical systems is often modeled as an inevitable thermodynamic slide toward equilibrium. However, we present evidence that this decay is fundamentally a noise-accumulation problem governed by spectral properties. Using novel pink noise generation methods, we demonstrate that structural coherence relies on the balance between “constructive entropy” (pink/1fnoise) and “destructive entropy” (Gaussian/white noise). We introduce the Pink-to-White Noise Ratio (PWNR) as a quantitative metric of systemic integrity and show through computational modeling that when PWNR exceeds a critical threshold, systems undergo a phase transition from entropic decay to structural rejuvenation. Our results suggest that “aging” in complex systems is not a fixed temporal vector but a reversible accumulation of spectral incoherence, with profound implications for control theory, network resilience, and non-equilibrium thermodynamics.Added the core contribution of an endogenous 1/f noise creator with the method to make it that's not white noise filtered.