Statistical physics of complex information dynamics

TL;DR

This paper introduces a unified statistical field theory framework for complex information dynamics, linking microscopic interactions to emergent phenomena like phase transitions and functional diversity in complex systems.

Contribution

It develops a physically-grounded, unified approach to model information exchange and emergent behaviors in complex networks, incorporating a density matrix and von Neumann entropy analysis.

Findings

von Neumann entropy measures functional diversity

Modularity and hierarchy promote functional diversity

Unified framework connects microscopic interactions to macroscopic phenomena

Abstract

The constituents of a complex system exchange information to function properly. Their signalling dynamics often leads to the appearance of emergent phenomena, such as phase transitions and collective behaviors. While information exchange has been widely modeled by means of distinct spreading processes -- such as continuous-time diffusion, random walks, synchronization and consensus -- on top of complex networks, a unified and physically-grounded framework to study information dynamics and gain insights about the macroscopic effects of microscopic interactions, is still eluding us. In this article, we present this framework in terms of a statistical field theory of information dynamics, unifying a range of dynamical processes governing the evolution of information on top of static or time varying structures. We show that information operators form a meaningful statistical ensemble and their superposition defines a density matrix that can be used for the analysis of complex dynamics. As a direct application, we show that the von Neumann entropy of the ensemble can be a measure of the functional diversity of complex systems, defined in terms of the functional differentiation of higher-order interactions among their components. Our results suggest that modularity and hierarchy, two key features of empirical complex systems -- from the human brain to social and urban networks -- play a key role to guarantee functional diversity and, consequently, are favored.