Spatial and Temporal Cluster Tomography of Active Matter

TL;DR

This paper introduces spatial and temporal cluster tomography as innovative tools for detecting and analyzing phase transitions in active matter systems, providing a higher-order alternative to traditional correlation functions.

Contribution

The authors develop and demonstrate spatial and temporal cluster tomography methods for characterizing phase transitions in active systems without relying on system-specific order parameters.

Findings

Cluster tomography effectively locates phase transitions in active matter.

Spatial features from cluster tomography can measure critical exponents.

Temporal cluster tomography captures dynamical behaviors via burstiness analysis.

Abstract

Critical phase transitions have proven to be a powerful concept to capture the phenomenology of many systems, including deeply non-equilibrium ones like living systems. The study of these phase transitions has overwhelmingly relied on two-point correlation functions. In this Letter, we show that cluster tomography -- the study of one-dimensional cross-sections of the clusters that emerge near a phase transition -- is an alternative higher-order tool that efficiently locates and characterizes phase transitions in active systems. First, using motility-induced phase separation as a paradigmatic example, we show how complex geometric features of clusters, captured by spatial cluster tomography, can be used to measure critical exponents in active systems without explicitly introducing system-specific order parameters. Second, we introduce temporal cluster tomography, an analogous cluster-based measurement that characterizes the dynamical behavior of active systems. We show that cluster dynamics can be captured by a generalization of burstiness analysis in complex temporal networks. Both spatial and temporal cluster tomography are easy to implement yet powerful approaches to study non-equilibrium systems, making them useful additions to the standard toolbox of statistical physics.