5,774 research outputs found
Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System
Peer reviewedPublisher PD
Statistical mechanics and information-theoretic perspectives on complexity in the Earth system
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 system Earth. Specifically, we discuss two classes of methods: (i) entropies of different kinds (e.g., on the one hand classical Shannon and R´enyi 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
Anomaly Detection in Paleoclimate Records using Permutation Entropy
Permutation entropy techniques can be useful in identifying anomalies in
paleoclimate data records, including noise, outliers, and post-processing
issues. We demonstrate this using weighted and unweighted permutation entropy
of water-isotope records in a deep polar ice core. In one region of these
isotope records, our previous calculations revealed an abrupt change in the
complexity of the traces: specifically, in the amount of new information that
appeared at every time step. We conjectured that this effect was due to noise
introduced by an older laboratory instrument. In this paper, we validate that
conjecture by re-analyzing a section of the ice core using a more-advanced
version of the laboratory instrument. The anomalous noise levels are absent
from the permutation entropy traces of the new data. In other sections of the
core, we show that permutation entropy techniques can be used to identify
anomalies in the raw data that are not associated with climatic or
glaciological processes, but rather effects occurring during field work,
laboratory analysis, or data post-processing. These examples make it clear that
permutation entropy is a useful forensic tool for identifying sections of data
that require targeted re-analysis---and can even be useful in guiding that
analysis.Comment: 15 pages, 7 figure
Quantum processes, space-time representation and brain dynamics
The recent controversy of applicability of quantum formalism to brain
dynamics has been critically analysed. The prerequisites for any type of
quantum formalism or quantum field theory is to investigate whether the
anatomical structure of brain permits any kind of smooth geometric notion like
Hilbert structure or four dimensional Minkowskian structure for quantum field
theory. The present understanding of brain function clearly denies any kind of
space-time representation in Minkowskian sense. However, three dimensional
space and one time can be assigned to the neuromanifold and the concept of
probabilistic geometry is shown to be appropriate framework to understand the
brain dynamics. The possibility of quantum structure is also discussed in this
framework.Comment: Latex, 28 page
Local Causal States and Discrete Coherent Structures
Coherent structures form spontaneously in nonlinear spatiotemporal systems
and are found at all spatial scales in natural phenomena from laboratory
hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary
climate dynamics. Phenomenologically, they appear as key components that
organize the macroscopic behaviors in such systems. Despite a century of
effort, they have eluded rigorous analysis and empirical prediction, with
progress being made only recently. As a step in this, we present a formal
theory of coherent structures in fully-discrete dynamical field theories. It
builds on the notion of structure introduced by computational mechanics,
generalizing it to a local spatiotemporal setting. The analysis' main tool
employs the \localstates, which are used to uncover a system's hidden
spatiotemporal symmetries and which identify coherent structures as
spatially-localized deviations from those symmetries. The approach is
behavior-driven in the sense that it does not rely on directly analyzing
spatiotemporal equations of motion, rather it considers only the spatiotemporal
fields a system generates. As such, it offers an unsupervised approach to
discover and describe coherent structures. We illustrate the approach by
analyzing coherent structures generated by elementary cellular automata,
comparing the results with an earlier, dynamic-invariant-set approach that
decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht
Debates: Does Information Theory Provide a New Paradigm for Earth Science? Emerging Concepts and Pathways of Information Physics
Entropy and Information are key concepts not only in Information Theory but also in Physics: historically in the fields of Thermodynamics, Statistical and Analytical Mechanics, and, more recently, in the field of Information Physics. In this paper we argue that Information Physics reconciles and generalizes statistical, geometric, and mechanistic views on information. We start by demonstrating how the use and interpretation of Entropy and Information coincide in Information Theory, Statistical Thermodynamics, and Analytical Mechanics, and how this can be taken advantage of when addressing Earth Science problems in general and hydrological problems in particular. In the second part we discuss how Information Physics provides ways to quantify Information and Entropy from fundamental physical principles. This extends their use to cases where the preconditions to calculate Entropy in the classical manner as an aggregate statistical measure are not met. Indeed, these preconditions are rarely met in the Earth Sciences due either to limited observations or the far-from-equilibrium nature of evolving systems. Information Physics therefore offers new opportunities for improving the treatment of Earth Science problems.info:eu-repo/semantics/publishedVersio
Preface - Personal perspectives in nonlinear science : Looking back, looking forward
Peer reviewedPublisher PD
- …