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March 14, 2026Open Access

Critical Transition and Reliability Boundary in a Constraint-Driven Non-Equilibrium Circulatory Update System

Key Points

This research aims to explore the critical transition and reliability boundary in a constraint-driven non-equilibrium circulatory update system.
Conducted numerical simulations to study the system behavior over varied control parameters.
Analyzed the statistical properties of spectral slopes during the simulations.
Estimated the critical parameter defining the reliability boundary.
Identified a significant transition in spectral slope properties as the control parameter varied.
Estimated critical parameter as η_c ≈ 6 × 10⁻⁶, delineating stability from instability in the system.

Abstract

This record contains the manuscript: "Critical Transition and Reliability Boundary in a Constraint-Driven Non-Equilibrium Circulatory Update System". The study investigates a constraint-driven non-equilibrium circulatory update system using numerical simulations. By sweeping the control parameter η across several orders of magnitude, a transition in the statistical properties of spectral slopes is observed. The transition separates stable system behavior from regimes where persistent irreversible response patterns emerge. From the statistical analysis, the critical parameter is estimated as ηc ≈ 6 × 10⁻⁶, which defines a reliability boundary in the parameter space of the system. The manuscript presents the numerical setup, statistical analysis, and characterization of this critical transition. Related work: Spectral Slope Branch Structure and Observational Localizationhttps: //doi. org/10. 5281/zenodo. 18987482

Critical Transition and Reliability Boundary in a Constraint-Driven Non-Equilibrium Circulatory Update System

Key Points

Abstract

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