Alexander F. Siegenfeld and Yaneer Bar-Yam

Entropy 2025, 27(8), 835

Ashby’s law of requisite variety allows a comparison of systems with their environments, providing a necessary (but not sufficient) condition for system efficacy: A system must possess at least as much complexity as any set of environmental behaviors that require distinct responses from the system. However, to account for the dependence of a system’s complexity on the level of detail—or scale—of its description, a multi-scale generalization of Ashby’s law is needed. We define a class of complexity profiles (complexity as a function of scale) that is the first, to our knowledge, to exhibit a multi-scale law of requisite variety. This formalism provides a characterization of multi-scale complexity and generalizes the law of requisite variety’s single constraint on system behaviors to a class of multi-scale constraints. We show that these complexity profiles satisfy a sum rule, which reflects a tradeoff between smaller- and larger-scale degrees of freedom, and we extend our results to subdivided systems and systems with a continuum of components.

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Samson Abramsky, Wolfgang Banzhaf, Leo S. D. Caves, Michael Levin, Penousal Machado, Charles Ofria, Susan Stepney, Roger White

Living systems exhibit a range of fundamental characteristics: they are active, self-referential, self-modifying systems. This paper explores how these characteristics create challenges for conventional scientific approaches and why they require new theoretical and formal frameworks. We introduce a distinction between ‘natural time’, the continuing present of physical processes, and ‘representational time’, with its framework of past, present and future that emerges with life itself. Representational time enables memory, learning and prediction, functions of living systems essential for their survival. Through examples from evolution, embryogenesis and metamorphosis we show how living systems navigate the apparent contradictions arising from self-reference as natural time unwinds self-referential loops into developmental spirals. Conventional mathematical and computational formalisms struggle to model self-referential and self-modifying systems without running into paradox. We identify promising new directions for modelling self-referential systems, including domain theory, co-algebra, genetic programming, and self-modifying algorithms. There are broad implications for biology, cognitive science and social sciences, because self-reference and self-modification are not problems to be avoided but core features of living systems that must be modelled to understand life’s open-ended creativity.

Read the full article at: arxiv.org

Laurent Hébert-Dufresne, Juniper Lovato, Giulio Burgio, James P. Gleeson, S. Redner, and P. L. Krapivsky
Phys. Rev. Lett. 135, 087401

Models of how things spread often assume that transmission mechanisms are fixed over time. However, social contagions—the spread of ideas, beliefs, innovations—can lose or gain in momentum as they spread: ideas can get reinforced, beliefs strengthened, products refined. We study the impacts of such self-reinforcement mechanisms in cascade dynamics. We use different mathematical modeling techniques to capture the recursive, yet changing nature of the process. We find a critical regime with a range of power-law cascade size distributions with nonuniversal scaling exponents. This regime clashes with classic models, where criticality requires fine-tuning at a precise critical point. Self-reinforced cascades produce critical-like behavior over a wide range of parameters, which may help explain the ubiquity of power-law distributions in empirical social data.

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Julia Schüler, Maik Bieleke, Matti T. J. Heino, Natalia Balague Serre, Angel Chater, Markus Gruber, Martina Kanning, Daniel A. Keim, Daniela Mier, Maria Moreno-Villanueva, Fridtjof Nussbeck, Jens C. Pruessner, Termeh Shafie, and Michael Schwenk

The rising of physical inactivity and its associated health and economic burdens persist de-spite decades of interdisciplinary research aimed at promoting physical activity (PA). This Per-spective takes a complex systems view on PA, proposing that at least two layers of complexity should be taken into account: 1) interactions between various physiological, psychological, social, and environmental systems and 2) their dynamic interactions across time. To address this complexity, all stages of the research process—from theory and measurement to study design, analysis, and interventions—must be aligned with a complex systems perspective. This alignment requires intensive interdisciplinary collaboration and an integration of basic and applied research beyond current research practices to create transdisciplinary solutions. We offer actionable insights that bridge the gap between abstract theoretical approaches (e.g., complex systems and attractor landscape frameworks of behavior change) and practical PA research, thereby laying a foundation for more effective behavior change interventions.

Read the full article at: osf.io