Anatomy of a Spin: The Information-Theoretic Structure of Classical Spin Systems

Vijayaraghavan, Vikram S.; James, Ryan G.; Crutchfield, James P.

doi:10.3390/e19050214

Cited by 12 publications

(12 citation statements)

References 50 publications

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“…In the case of ferromagnetic Ising models, [2] show numerically that this transfer entropy is maximized in the disordered phase, that is, in the region where only one invariant measure exists and which would correspond to the subcritical regime for the contact process. This result is confirmed by the findings of [16]. [2] argue that their result could be related to a subtle interplay between sites within and out the boundaries of same spin domains whose probability distributions are a function of the temperature.…”

Section: Final Discussionsupporting

confidence: 73%

Information Transmission and Criticality in the Contact Process

2017

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Abstract. In the present paper, we study the relation between criticality and information transmission in the one-dimensional contact process with infection parameter λ. We introduce a notion of sensitivity of the process to its initial condition and prove that it increases not only for values of λ < λc, the value of the critical parameter, but keeps increasing even after λc, before finally starting to decrease for values of λ sufficiently above λc. This provides a counterexample to the common belief that associates maximal information transmission to criticality.

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Section: Final Discussionsupporting

confidence: 73%

Information Transmission and Criticality in the Contact Process

2017

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“…As an example, consider the problem of determining "causal pathways" in a network [37,38]. 3 Given two paths between two network nodes, say A → B → C and A → B → C, one would like to determine through which pathway A's behavior most strongly influences C. This pathway is termed the causal pathway. Naïvely, one might assume that the pathway whose links are strongest is the more influential pathway or that it is the pathway maximizing a multivariate information measure.…”

Section: B Quantifying Dependenciesmentioning

confidence: 99%

Unique information via dependency constraints

James¹,

Emenheiser²,

Crutchfield³

2018

J. Phys. A: Math. Theor.

Self Cite

111

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The partial information decomposition (PID) is perhaps the leading proposal for resolving information shared between a set of sources and a target into redundant, synergistic, and unique constituents. Unfortunately, the PID framework has been hindered by a lack of a generally agreed-upon, multivariate method of quantifying the constituents. Here, we take a step toward rectifying this by developing a decomposition based on a new method that quantifies unique information. We first develop a broadly applicable method-the dependency decomposition-that delineates how statistical dependencies influence the structure of a joint distribution. The dependency decomposition then allows us to define a measure of the information about a target that can be uniquely attributed to a particular source as the least amount which the source-target statistical dependency can influence the information shared between the sources and the target. The result is the first measure that satisfies the core axioms of the PID framework while not satisfying the Blackwell relation, which depends on a particular interpretation of how the variables are related. This makes a key step forward to a practical PID. PACS numbers: 05.45.-a 89.75.Kd 89.70.+c 02.50.-r

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“…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.…”

Section: Scope Of This Work and Contributionmentioning

confidence: 99%

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

Rosas

Mediano

Ugarte

2018

Entropy

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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...

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Anatomy of a Spin: The Information-Theoretic Structure of Classical Spin Systems

Cited by 12 publications

References 50 publications

Information Transmission and Criticality in the Contact Process

Information Transmission and Criticality in the Contact Process

Unique information via dependency constraints

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

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