Statistical physics of complex information dynamics

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.

arXiv comment7 pages, 3 figures

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• Does the brain behave like a (complex) network? I. Dynamics
• Multilayer Network Science: from Cells to Societies
• Unraveling the effects of multiscale network entanglement on disintegration of empirical systems
• Laplacian paths in complex networks: information core emerges from entropic transitions
• Information propagation in multilayer systems with higher-order interactions across timescales
• Generalized network density matrices for analysis of multiscale functional diversity
• Network Renormalization
• Uncovering hidden dependency in weighted networks via information entropy
• Grand canonical ensembles of sparse networks and Bayesian inference
• Multi-scale Laplacian community detection in heterogeneous networks
• Laplacian Renormalization Group: An introduction to heterogeneous coarse-graining
• Emergent information dynamics in many-body interconnected systems
• Statistical physics of exchangeable sparse simple networks, multiplex networks and simplicial complexes
• A measure of dissimilarity between diffusive processes on networks
• Dissimilarity between synchronization processes on networks
• Latent geometry emerging from network-driven processes