We introduce structural inertia mIDT (u) = (uᵀGu) / (uᵀHu) for stable regimes of the Information-Dynamic Theory (IDT) gradient flow dω/dτ = −G⁻¹∇Φ. We prove that structural inertia equals the inverse relaxation time along eigenmodes of the linearized dynamics. The resulting spectrum characterizes the relaxation geometry of regimes on Fisher-metric manifolds. An explicit Gaussian example demonstrates how non-flat Fisher geometry modifies the relaxation spectrum relative to standard Hessian analysis. Structural inertia is proposed as a geometric invariant describing regime stability in the IDT framework.
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Aleksei Sadovnikov
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Aleksei Sadovnikov (Wed,) studied this question.
www.synapsesocial.com/papers/69b3ad0502a1e69014ccf366 — DOI: https://doi.org/10.5281/zenodo.18948974