English

Phase transition revealed by eigen microstate entropy

Statistical Mechanics 2025-12-30 v1 Adaptation and Self-Organizing Systems

Abstract

We introduce the eigen microstate entropy (SEMS_{\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 SEMS_{\text{EM}} to non-equilibrium complex systems. Our analysis reveals a consistent precursor signal: a significant increase in SEMS_{\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 SEMS_{\text{EM}} as a general framework for detecting and interpreting phase transitions in non-equilibrium systems.

Keywords

Cite

@article{arxiv.2512.23086,
  title  = {Phase transition revealed by eigen microstate entropy},
  author = {Teng Liu and Xuezhi Niu and Mingli Zhang and Gaoke Hu and Yuhan Chen and Yongwen Zhang and Rui Shi and Jingyuan Li and Peng Tan and Maoxin Liu and Hui Li and Xiaosong Chen},
  journal= {arXiv preprint arXiv:2512.23086},
  year   = {2025}
}
R2 v1 2026-07-01T08:43:40.966Z