What question did this study set out to answer?

The aim is to clarify the concept of structural inertia within the framework of Information-Dynamic Theory (IDT) and its implications on regime stability.

March 13, 2026Open Access

Structural Inertia and Relaxation Geometry in Information-Dynamic Theory

Key Points

The aim is to clarify the concept of structural inertia within the framework of Information-Dynamic Theory (IDT) and its implications on regime stability.
Introduced structural inertia m_IDT(u) as a ratio using mathematical definitions from IDT.
Proved the equivalence of structural inertia and inverse relaxation time along eigenmodes.
Analyzed the relaxation geometry on Fisher-metric manifolds using a Gaussian example.
Structural inertia accurately represents the inverse relaxation time in eigenmodes of linearized dynamics.
The spectrum derived from the analysis characterizes the relaxation geometry on Fisher-metric manifolds.
Non-flat Fisher geometry alters the relaxation spectrum compared to traditional Hessian analysis.

Abstract

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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Structural Inertia and Relaxation Geometry in Information-Dynamic Theory

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