ArticleEntropy (Basel, Switzerland)2026
What Is a Pattern in Statistical Mechanics? Formalizing Structure and Patterns in One-Dimensional Spin Lattice Models with Computational Mechanics.
Article in Entropy (Basel, Switzerland), 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.
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1 citing paper in PubMed.
- Thermodynamic Insights into the Impact of Increasing Connectivity for 2D-Lattices Based on Ising Chains.Entropy (Basel, Switzerland) · 2026Article
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Abstract
This work formalizes the notions of structure and pattern for three distinct one-dimensional spin-lattice models (finite-range Ising, solid-on-solid, and three-body), using information- and computation-theoretic methods. We begin by presenting a novel derivation of the Boltzmann distribution for finite one-dimensional spin configurations embedded in infinite ones. We next recast this distribution as a stochastic process, thereby enabling us to analyze each spin-lattice model within the theory of computational mechanics. In this framework, the process's structure is quantified by excess entropy E (predictable information) and statistical complexity Cμ (stored information), and the process's structure-generating mechanism is specified by its ϵ-machine. To assess compatibility with statistical mechanics, we compare the configurations jointly determined by the information measures and ϵ-machines to typical configurations drawn from the Boltzmann distribution, and we find agreement. We also include a self-contained primer on computational mechanics and provide code implementing the information measures and spin-model distributions.
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