Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Abstract

This review provides a summary of methods originated in (non-equilibrium) statistical mechanics and information theory, which have recently found successful applications to quantitatively studying complexity in various components of the complex Entropy 2013, 15 4845 system Earth. Specifically, we discuss two classes of methods: (i) entropies of different kinds (e.g., on the one hand classical Shannon and Rényi entropies, as well as non-extensive Tsallis entropy based on symbolic dynamics techniques and, on the other hand, approximate entropy, sample entropy and fuzzy entropy); and (ii) measures of statistical interdependence and causality (e.g., mutual information and generalizations thereof, transfer entropy, momentary information transfer). We review a number of applications and case studies utilizing the above-mentioned methodological approaches for studying contemporary problems in some exemplary fields of the Earth sciences, highlighting the potentials of different techniques.

Unified functional network and nonlinear time series analysis for complex systems science: Thepyunicornpackage

“…Note, however, that reliable causal analyses, especially with information-theoretic estimators, require much more samples than classical bivariate analysis, which typically restricts their applicability to much smaller networks. 88 An alternative to classical path-based network measures is discussed by Runge et al 89 and Runge, 90 and introduces quantifiers of information transfer through causal pathways.…”

Entropies from Markov Models as Complexity Measures of Embedded Attractors

“…Although some information-theoretic-based works make no explicit reference to Takens' theorem when defining complexity measures, since the early work by Pincus [5], it is clear that the vectors used for the estimation of the correlation sum can be understood as points obtained from a reconstructed state space with the embedding dimension set by default to two and time delay set to one. This idea is also set by Balasis et al [4], considering that several of the most well-known information-theoretic measures used as complexity measures can also be considered as phase space-based approaches. An important fact of Takens' theorem is that it demonstrates that under very general conditions, the reconstructed state space contains most of the information of the original state space and also that the mapping between these two spaces is smooth and invertible, i.e., the reconstructed state space is a diffeomorphic version of the original one [6].…”

“…These effects cannot be characterized using standard methods of signal analysis, which are commonly based on linear assumptions about the dynamics of the system under study [1] (Chapter 1). This kind of analysis has proven to be very useful for characterizing pathophysiological conditions using different biomedical signals [2], for quantifying machinery health conditions [3], Earth science [4] and many other fields of application.…”

Recent seismic activity at Cephalonia (Greece): a study through candidate electromagnetic precursors in terms of non-linear dynamics

“…The possible relation of the field-observed fracture-induced electromagnetic emissions (EME) in the frequency bands of MHz and kHz, associated with shallow EQs with magnitude 6 or larger that oc-curred inland or near the coast, has been examined in a series of publications in order to contribute to a better understanding of the underlying processes (e.g. Eftaxias et al, 2001Eftaxias et al, , 2004Eftaxias et al, , 2008Kapiris et al, 2004;Karamanos et al, 2006;Papadimitriou et al, 2008;Contoyiannis et al, 2005Contoyiannis et al, , 2013Potirakis et al, 2011Potirakis et al, , 2012aPotirakis et al, , b, c, 2013Potirakis et al, , 2015Minadakis et al, 2012a, b;Balasis et al, 2011Balasis et al, , 2013Donner et al, 2015;Kalimeris et al, 2016). Additionally, a four-stage model for the preparation of an EQ by means of its observable EM activity has been recently put forward Contoyiannis et al, 2015, and references therein).…”