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A defining property of complex systems is that they have multiscale structure. How does this multiscale structure come about? We argue that within systems there emerges a hierarchy of scales that contribute to a system's causal workings. An…

Information Theory · Computer Science 2025-10-15 Abel Jansma , Erik Hoel

Emergence and causality are two fundamental concepts for understanding complex systems. They are interconnected. On one hand, emergence refers to the phenomenon where macroscopic properties cannot be solely attributed to the cause of…

Physics and Society · Physics 2024-02-27 Bing Yuan , Zhang Jiang , Aobo Lyu , Jiayun Wu , Zhipeng Wang , Mingzhe Yang , Kaiwei Liu , Muyun Mou , Peng Cui

Causal emergence is the theory that macroscales can reduce the noise in causal relationships, leading to stronger causes at the macroscale. First identified using the effective information and later the integrated information in model…

Physics and Society · Physics 2022-02-07 Renzo Comolatti , Erik Hoel

The broad concept of emergence is instrumental in various of the most challenging open scientific questions -- yet, few quantitative theories of what constitutes emergent phenomena have been proposed. This article introduces a formal theory…

Neurons and Cognition · Quantitative Biology 2021-01-27 Fernando E. Rosas , Pedro A. M. Mediano , Henrik J. Jensen , Anil K. Seth , Adam B. Barrett , Robin L. Carhart-Harris , Daniel Bor

Beneficial to advanced computing devices, models with massive parameters are increasingly employed to extract more information to enhance the precision in describing and predicting the patterns of objective systems. This phenomenon is…

Information Theory · Computer Science 2024-03-08 Liye Jia , Fengyufan Yang , Ka Lok Man , Erick Purwanto , Sheng-Uei Guan , Jeremy Smith , Yutao Yue

Emergence, the phenomena where a system's micro-scale dynamics facilitate the development of non-trivial, informative higher scales, has become a foundational concept in modern sciences, tying together fields as diverse as physics, biology,…

Cellular Automata and Lattice Gases · Physics 2020-03-31 Thomas F. Varley

Understanding the functional architecture of complex systems is crucial to illuminate their inner workings and enable effective methods for their prediction and control. Recent advances have introduced tools to characterise emergent…

Adaptation and Self-Organizing Systems · Physics 2024-06-06 Fernando E. Rosas , Bernhard C. Geiger , Andrea I Luppi , Anil K. Seth , Daniel Polani , Michael Gastpar , Pedro A. M. Mediano

The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…

Materials Science · Physics 2025-09-30 Elisabetta Nocerino

A central challenge in the study of complex systems is the quantification of emergence -- understood as the ability of the system to exhibit collective behaviours that cannot be traced down to the individual components. While recent work…

Many systems involve numerous interacting parts and the whole system can have properties that the individual parts do not. I take this novelty as the defining characteristic of an emergent property. Other characteristics associated with…

History and Philosophy of Physics · Physics 2025-11-05 Ross H. McKenzie

The causal structure of any system can be analyzed at a multitude of spatial and temporal scales. It has long been thought that while higher scale (macro) descriptions of causal structure may be useful to observers, they are at best a…

Information Theory · Computer Science 2017-05-24 Erik P Hoel

Emergence is a profound subject that straddles many scientific disciplines, including the formation of galaxies and how consciousness arises from the collective activity of neurons. Despite the broad interest that exists on this concept,…

Consciousness spans macroscopic experience and microscopic neuronal activity, yet linking these scales remains challenging. Prevailing theories, such as Integrated Information Theory, focus on a single scale, overlooking how causal power…

Neurons and Cognition · Quantitative Biology 2025-09-16 Zhipeng Wang , Yingqi Rong , Kaiwei Liu , Mingzhe Yang , Jiang Zhang , Jing He

We present a domain-general account of causation that applies to settings in which macro-level causal relations between two systems are of interest, but the relevant causal features are poorly understood and have to be aggregated from vast…

Machine Learning · Statistics 2015-12-29 Krzysztof Chalupka , Pietro Perona , Frederick Eberhardt

Concurrent systems identify systems, either software, hardware or even biological systems, that are characterized by sets of independent actions that can be executed in any order or simultaneously. Computer scientists resort to a causal…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-03-07 Silvia Crafa , Federica Russo

The description of the dynamics of complex systems, in particular the capture of the interaction structure and causal relationships between elements of the system, is one of the central questions of interdisciplinary research. While the…

Machine Learning · Statistics 2025-04-30 Jakub Kořenek , Pavel Sanda , Jaroslav Hlinka

Distributed systems often exhibit emergent behaviors that impact their resilience (Franz-Kaiser et al., 2020; Adilson E. Motter, 2002; Jianxi Gao, 2016). This paper presents a theoretical framework combining attributed graph models,…

Systems and Control · Electrical Eng. & Systems 2025-03-19 Anatoly A. Krasnovsky

The claim that life is an emergent phenomenon exhibiting novel properties and principles is often criticized for being in conflict with causal closure at the microscopic level. I argue that advances in cosmological theory suggesting an…

Astrophysics · Physics 2007-05-23 P. C. W. Davies

Causal discovery, the task of automatically constructing a causal model from data, is of major significance across the sciences. Evaluating the performance of causal discovery algorithms should ideally involve comparing the inferred models…

Artificial Intelligence · Computer Science 2021-08-26 Maxime Peyrard , Robert West

After coarse-graining a complex system, the dynamics of its macro-state may exhibit more pronounced causal effects than those of its micro-state. This phenomenon, known as causal emergence, is quantified by the indicator of effective…

Information Theory · Computer Science 2025-02-13 Kaiwei Liu , Bing Yuan , Jiang Zhang
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