Maximum entropy network states for coalescence processes

TL;DR

This paper introduces a maximum entropy framework for characterizing complex network states with heterogeneous connectivity and dynamics, analyzing coalescence processes and their transitions across different temporal scales.

Contribution

It proposes a novel maximum entropy principle for network states, applicable to systems with complex, correlated connectivity and dynamics, and analyzes their entropy and phase transitions.

Findings

Characterizes entropy in three coalescence processes.

Identifies dynamical regime transitions across temporal scales.

Provides a framework for studying interconnected and active matter systems.

Abstract

Complex network states are characterized by the interplay between system's structure and dynamics. One way to represent such states is by means of network density matrices, whose von Neumann entropy characterizes the number of distinct microstates compatible with given topology and dynamical evolution. In this Letter, we propose a maximum entropy principle to characterize network states for systems with heterogeneous, generally correlated, connectivity patterns and non-trivial dynamics. We focus on three distinct coalescence processes, widely encountered in the analysis of empirical interconnected systems, and characterize their entropy and transitions between distinct dynamical regimes across distinct temporal scales. Our framework allows one to study the statistical physics of systems that aggregate, such as in transportation infrastructures serving the same geographic area, or correlate, such as inter-brain synchrony arising in organisms that socially interact, and active matter that swarm or synchronize.