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This paper aims to establish a refined classification system for complex-system phase transitions with three distinct layers.

August 11, 2026Open Access

Three Layers in the Classification of Complex-System Phase Transitions Thermodynamic, Spatial, and Engineering Criteria

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Randomized trial evaluates thermodynamic, spatial, and engineering criteria in complex-system transitions, suggesting new classification methods.

This paper aims to establish a refined classification system for complex-system phase transitions with three distinct layers.
Developed a three-layer classification framework.
Made corrections and completions to prior versions, adjusting definitions and parameters.
Revised theoretical models based on feedback loops and causal chains.
Classified phase transition types into thermodynamic, spatial, and engineering criteria.
Identified critical points, including the maxwell point at a specified value, enhancing predictive accuracy.
Recorded distinctions in cell types within the phase diagram, clarifying boundaries and classifications.

Qinfu Li (2026) studied this question.

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Randomized trial evaluates thermodynamic, spatial, and engineering criteria in complex-system transitions, suggesting new classification methods.