Statistical physics of complex information dynamics.

The constituents of a complex system exchange information to function properly. Their signaling 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 paper, 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.

[1]  Heiko Rieger,et al.  Random walks on complex networks. , 2004, Physical review letters.

[2]  Daniel M. Conti,et al.  Dynamic scaling in natural swarms , 2016, Nature Physics.

[3]  Manlio De Domenico,et al.  Enhancing transport properties in interconnected systems without altering their structure , 2020, Physical Review Research.

[4]  Mark E. J. Newman.  A measure of betweenness centrality based on random walks , 2005, Soc. Networks.

[5]  Danna Zhou,et al.  d. , 1934, Microbial pathogenesis.

[6]  Emilio Ferrara,et al.  Bots increase exposure to negative and inflammatory content in online social systems , 2018, Proceedings of the National Academy of Sciences.

[7]  Albert-László Barabási,et al.  Hierarchical organization in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Duncan J Watts,et al.  A simple model of global cascades on random networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Manlio De Domenico,et al.  Diffusion geometry unravels the emergence of functional clusters in collective phenomena , 2017, Physical review letters.

[10]  Michel Loreau,et al.  Functional diversity governs ecosystem response to nutrient enrichment , 2000, Nature.

[11]  Shigeo Sato,et al.  Impact of modular organization on dynamical richness in cortical networks , 2018, Science Advances.

[12]  C. Hilgetag,et al.  Hierarchical modular brain connectivity is a stretch for criticality , 2014, Trends in Cognitive Sciences.

[13]  Shun-ichi Amari,et al.  A method of statistical neurodynamics , 1974, Kybernetik.

[14]  Michael L. Anderson,et al.  Describing functional diversity of brain regions and brain networks , 2013, NeuroImage.

[15]  Klaas E. Stephan,et al.  Network participation indices: characterizing component roles for information processing in neural networks , 2003, Neural Networks.

[17]  Mason A. Porter,et al.  Random walks and diffusion on networks , 2016, ArXiv.

[18]  Naoki Masuda,et al.  Temporal networks: slowing down diffusion by long lasting interactions , 2013, Physical review letters.

[19]  Karl J. Friston,et al.  Structural and Functional Brain Networks: From Connections to Cognition , 2013, Science.

[20]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[21]  Martin Rosvall,et al.  Maps of random walks on complex networks reveal community structure , 2007, Proceedings of the National Academy of Sciences.

[22]  Albert-László Barabási,et al.  Universal resilience patterns in complex networks , 2016, Nature.

[23]  Manlio De Domenico,et al.  Spectral entropies as information-theoretic tools for complex network comparison , 2016, 1609.01214.

[24]  W. Bialek,et al.  Statistical mechanics for natural flocks of birds , 2011, Proceedings of the National Academy of Sciences.

[25]  Guy B. Williams,et al.  Consciousness-specific dynamic interactions of brain integration and functional diversity , 2019, Nature Communications.

[26]  Baruch Barzel,et al.  Dynamic patterns of information flow in complex networks , 2017, Nature Communications.

[27]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[28]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[29]  J. Herskowitz,et al.  Proceedings of the National Academy of Sciences, USA , 1996, Current Biology.

[30]  Conrado J. Pérez Vicente,et al.  Diffusion dynamics on multiplex networks , 2012, Physical review letters.

[31]  Marian Stamp Dawkins,et al.  The Noisy Brain: Stochastic Dynamics as a Principle of Brain Function The Noisy Brain: Stochastic Dynamics as a Principle of Brain Function. By Edmund T. Rolls & Gustavo Deco. Oxford: Oxford University Press (2010). Pp. 310. Price £37.95 hardback. , 2010, Animal Behaviour.

[32]  Edward T. Bullmore,et al.  Modular and Hierarchically Modular Organization of Brain Networks , 2010, Front. Neurosci..

[33]  Changsong Zhou,et al.  Hierarchical organization unveiled by functional connectivity in complex brain networks. , 2006, Physical review letters.

[34]  Mason A. Porter,et al.  Author Correction: The physics of spreading processes in multilayer networks , 2016, 1604.02021.