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arXiv · 2512.23086

Phase transition revealed by eigen microstate entropy

Teng Liu·Xuezhi Niu·Mingli Zhang·Gaoke Hu·Yuhan Chen·Yongwen Zhang·Rui Shi·Jingyuan Li·Peng Tan·Maoxin Liu·Hui Li·Xiaosong Chen
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Abstract

We introduce the eigen microstate entropy ($S_{\text{EM}}$), a novel metric of complexity derived from the probabilities of statistically independent eigen microstates. After establishing its scaling behavior in equilibrium systems and demonstrating its utility in critical phenomena (mean spherical, Ising, and Potts models), we apply $S_{\text{EM}}$ to non-equilibrium complex systems. Our analysis reveals a consistent precursor signal: a significant increase in $S_{\text{EM}}$ precedes major phase transitions. Specifically, we observe this entropy rise before biomolecular condensate formation in liquid-liquid phase separation in living cells and months ahead of El Ni\~no events. These findings position $S_{\text{EM}}$ as a general framework for detecting and interpreting phase transitions in non-equilibrium systems.

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Teng Liu, Xuezhi Niu, Mingli Zhang, Gaoke Hu, Yuhan Chen, Yongwen Zhang, Rui Shi, Jingyuan Li, Peng Tan, Maoxin Liu, Hui Li, Xiaosong Chen. 2025-12-28. Phase transition revealed by eigen microstate entropy. https://arxiv.org/abs/2512.23086

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