Abstract
We discuss the problem of quantifying complexity in the framework of a hierarchical modelling of physical systems. The analysis is first performed on the set of all symbolic sequences which label non-empty regions in phase-space. A dynamical process represented by a shift map is associated with each admissible doubly-infinite sequence. The “grammatical” rules governing it are unfolded by using variable-length prefix-free codewords and described by means of allowed transitions on a “logic” tree. The derived model is employed to make predictions about the scaling behaviour of the system’s observables at each level of resolution. The complexity of the system, relative to the unfolding scheme, is evaluated through a generalization of the information gain by comparing prediction and observation. Rapidly converging estimates of thermodynamic averages can be obtained from the logic tree in the general incomplete-folding case using a transfer-matrix technique, related to the theory of scaling functions.
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© 1991 Plenum Press, New York
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Badii, R., Finardi, M., Broggi, G. (1991). Unfolding Complexity and Modelling Asymptotic Scaling Behavior. In: Artuso, R., Cvitanović, P., Casati, G. (eds) Chaos, Order, and Patterns. NATO ASI Series, vol 280. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0172-2_12
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DOI: https://doi.org/10.1007/978-1-4757-0172-2_12
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