Phase transition revealed by eigen microstate entropy

TL;DR

The paper introduces eigen microstate entropy ($S_{ ext{EM}}$), a new complexity measure that detects phase transitions in both equilibrium and non-equilibrium systems, including biological and climate phenomena.

Contribution

It presents $S_{ ext{EM}}$ as a novel metric for identifying phase transitions, demonstrating its effectiveness across various models and real-world systems.

Findings

$S_{ ext{EM}}$ increases before phase transitions in models.

Precursor signals detected in biological condensates.

Early warning signals for El Niño events.

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.