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Entropy 2017, 19(5), 214; doi:10.3390/e19050214

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

Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA
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Academic Editors: Kevin H. Knuth and Ariel Caticha
Received: 22 January 2017 / Revised: 22 March 2017 / Accepted: 3 May 2017 / Published: 8 May 2017
(This article belongs to the Section Statistical Mechanics)
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Abstract

Collective organization in matter plays a significant role in its expressed physical properties. Typically, it is detected via an order parameter, appropriately defined for each given system’s observed emergent patterns. Recent developments in information theory, however, suggest quantifying collective organization in a system- and phenomenon-agnostic way: decomposing the system’s thermodynamic entropy density into a localized entropy, that is solely contained in the dynamics at a single location, and a bound entropy, that is stored in space as domains, clusters, excitations, or other emergent structures. As a concrete demonstration, we compute this decomposition and related quantities explicitly for the nearest-neighbor Ising model on the 1D chain, on the Bethe lattice with coordination number k = 3 , and on the 2D square lattice, illustrating its generality and the functional insights it gives near and away from phase transitions. In particular, we consider the roles that different spin motifs play (in cluster bulk, cluster edges, and the like) and how these affect the dependencies between spins. View Full-Text
Keywords: Ising spin model; thermodynamic entropy density; dual total correlation; entropy rate; elusive information; enigmatic information; predictable information rate; complex system Ising spin model; thermodynamic entropy density; dual total correlation; entropy rate; elusive information; enigmatic information; predictable information rate; complex system
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Vijayaraghavan, V.S.; James, R.G.; Crutchfield, J.P. Anatomy of a Spin: The Information-Theoretic Structure of Classical Spin Systems. Entropy 2017, 19, 214.

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