Spacial correlation in active matter*

The non-equilibrium properties of life have been deeply intriguing, and one promising approach to understanding these properties lies in the study of active matter. In biological systems, collective behavior often manifests in intricate dynamics. Collective cell groups display organized migration patterns, including vortex or parallel flows, which show apparent correlation properties. The mechanisms underlying collective cell movement depend on both intrinsic correlations within the cells and extrinsic correlations shaped by environmental factors, including the size of the confinements.

These correlations not only influence dynamic cell migration but also play a pivotal role in collective cell alignment. Correlation among cells in a monolayer is fundamental for generating topological defects, which in turn drive tissue morphogenesis. The correlation function serves as an indispensable analytical tool, shedding light on the nuances of collective cell behaviors and facilitating a deeper comprehension of complex biological systems. Though correlation as a concept has long been used in statistical physics to describe the statistical relationship between random variables about spatial or temporal distance, its potential within the realm of biology remains underexplored.

In this study, we delve into the intricacies of correlations in collective cell systems. Our objective is to clarify ambiguities related to the definition of the correlation function within biomechanics. By identifying and rectifying prevalent inconsistencies, we aspire to enhance the interpretation clarity of correlations in the active matter realm. Our ultimate aim is to provide the biophysical community with insightful perspectives on the significance of correlations in steering active matters.