txt Thin Entropy, Thick Chaos: Transport, Fractals, and the Geometry of Dynamical Failure
por Doug M Doucette
Descrição do livro
This book argues that classical chaos theory—Lyapunov exponents, entropy, and fractal dimension—answers whether chaos exists but not what chaos can do. The missing variable is transport. Central distinction: Thin chaos = local instability + entropy production + fractal geometry that remains confined within a coherent operational region. The system is chaotic but stable (e.g., chaotic Trojan libration without escape, laser jitter without loss of lock). Thick chaos = local instability + entropy production + fractal geometry that becomes connected to failure-scale transport. Chaos becomes dangerous when it connects across functional boundaries. Three key revisions: Entropy needs location — distinguish internal entropy (harmless, confined) from transport entropy (appears in variables that define failure). Fractal dimension needs transport — distinguish internal fractal geometry (wrinkles inside coherence) from transport fractal geometry (tears that form pathways to failure). The classical triangle (stretching → entropy → fractal dimension) gains a fourth vertex: transport thickness. Operational diagnostic: The thinness ratio Θ = (chaotic transport scale)/(distance to failure). Θ ≪ 1 with λ>0 = thin chaos; Θ ≳ 1 with connectivity = thick chaos. Central message: Chaos is not automatically failure. Entropy is not automatically degradation. Fractal dimension is not automatically danger. Complexity becomes dangerous when it connects.
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