An Information-Theoretic Approach to Self-Organisation: Emergence of Complex Interdependencies in Coupled Dynamical Systems

Abstract

Self-organisation lies at the core of fundamental but still unresolved scientific questions, and holds the promise of de-centralised paradigms crucial for future technological developments. While self-organising processes have been traditionally explained by the tendency of dynamical systems to evolve towards specific configurations, or attractors, we see self-organisation as a consequence of the interdependencies that those attractors induce. Building on this intuition, in this work we develop a theoretical framework for understanding and quantifying self-organisation based on coupled dynamical systems and multivariate information theory. We propose a metric of global structural strength that identifies when self-organisation appears, and a multi-layered decomposition that explains the emergent structure in terms of redundant and synergistic interdependencies. We illustrate our framework on elementary cellular automata, showing how it can detect and characterise the emergence of complex structures. I see it" logic, which might eventually prevent further systematic developments [24]. Formulating formal definitions of self-organisation is challenging, partly because self-organisation has been used in diverse contexts and with different purposes [25], and partly due to the fact that the basic notions of "self" and "organisation" are already problematic themselves [26].The absence of an agreed formal definition, combined with the relevance of this notion for scientific and technological advances, generates a need for further explorations about the principles of self-organisation. Scope of this Work and ContributionIn the spirit of Reference [27], we explore to what extent an information-theoretic perspective can illuminate the inner workings of self-organising processes. Due to the connections between information theory and thermodynamics [28,29], our approach can be seen as an extension of previous works that relate self-organisation and statistical physics (see e.g. [30][31][32]). In previous research, self-organisation has been associated with a reduction in the system's entropy [30,33,34] -in contrast, we argue that entropy reduction alone is not a robust predictor of self-organisation, and additional metrics are required.This work establishes a way of understanding self-organising processes that is consistent with the Bayesian interpretation of information theory, as described in Reference [28]. One contribution of our approach is to characterise self-organising processes using multivariate information-theoretic toolsor, put differently, to provide a more fine-grained description of the underlying phenomena behind entropy reduction. We propose that self-organising processes are driven by spontaneous creation of interdependencies, while the reduction of entropy is a mere side effect of this. Following this rationale, we propose the binding information [35] as a metric of the strength of the interdependencies in out-of-equilibrium dynamical systems.Another contribution of our framework is to propose a multi-layer...

Quantifying high-order interdependencies via multivariate extensions of the mutual information

“…The growth profile of this non-decreasing function was taken as an indicator of the leading quality of the interdependency structure of X n , being convexity associated with statistical synergy, and concavity with redundancy [46,Definition 2].…”

“…Our results show a good agreement between these two metrics, which confirms the analytic reasoning presented above. In summary, Ω can be regarded as a formalisation of the intuitive notions introduced in [46]. Moreover, Ω possesses more theoretical properties than Ψ and requires the calculation of a smaller number of terms.…”

Topological Analysis of Differential Effects of Ketamine and Propofol Anesthesia on Brain Dynamics

“…One possible interpretation is that cycles can be thought of as "higher order dependencies" involving multiple channels. Rosas et al, describe patterns as "deviations from independence" [49], suggesting that an EPC with no cycles is one where all dimensions (i.e. channels) operate independently of one another through time.…”

Universality Classes and Information-Theoretic Measures of Complexity via Group Entropies

“…An influential example is Tononi's Integrated Information Theory [33,2], which suggests that consciousness can be detected from measures based on Shannon's entropy which by decompositions analyse the relationship if the information stored in the whole and in parts. A related very recent approach seeks to analyse self-organisation of synergetic interdependencies by a focus on joint Shannon entropies [21]. And finally let us mention the recent Entropic Brain Hypothesis [5], which relates increased consciousness to increase in the Shannon entropy, with less emphasis on how the interdependence of the conscious state is to be characterised.…”