What question did this study set out to answer?

This research aims to understand the role of ocean worlds as stable systems capable of sustaining complex processes over time.

March 12, 2026Open Access

GCST Framework for Ocean Worlds, Galactic Stability, and Cosmological Complexity Limits Planets-Oceans as Long-Lived Resonators of Complexity in the Universe

Key Points

This research aims to understand the role of ocean worlds as stable systems capable of sustaining complex processes over time.
Applied Global Complexity Stability Theory (GCST) and Optimal System Dynamics (OSD v1.2) to analyze ocean worlds.
Examined field equations governing instability dynamics in subsurface ocean moons and exoplanets.
Developed a theoretical framework incorporating principles of entropy, evolution, and complexity limits.
Identified ocean worlds as attractors of long-lived complexity due to their stability conditions.
Established hierarchical bounds on complexity that expand to galactic and cosmological scales.
Formulated a unified scale-invariant equation that reflects the emergence of complexity across the universe.

Abstract

Abstract Ocean worlds — including subsurface ocean moons and Hycean-type exoplanets — represent a special class of planetary systems with exceptional thermodynamic longevity. Within Global Complexity Stability Theory (GCST) and Optimal System Dynamics (OSD v1. 2), such worlds can be viewed as large-scale dissipative structures capable of sustaining complex self-organizing processes over extremely long timescales. The dynamics of instability are governed by the field equation: ∂Ψ/∂t = D ∇² Ψ + C α − γ Ψ with stability condition γ / (α C) > 1. Ocean planets operate in the deeply stable regime α ≪ 1, γ ≫ 1, making them natural attractors of long-lived complexity. Extending GCST to galactic and cosmological scales reveals hierarchical bounds on complexity: Cₘax ∝ γ / α at each level. A unified scale-invariant GCST equation emerges, while the variational principle, entropy law, evolution law, phase transitions, and information principle complete a self-consistent theoretical framework for the emergence and limits of complexity across cosmic scales.

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