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Entropy, Volume 10, Issue 4 (December 2008) – 23 articles , Pages 391-798

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Article
Thermal Contact
Entropy 2008, 10(4), 786-798; https://doi.org/10.3390/e10040786 - 22 Dec 2008
Cited by 7 | Viewed by 6231
Abstract
The concepts of temperature and entropy as applied in equilibrium thermodynamics do not easily generalize to nonequilibrium systems and there are transient systems where thermodynamics cannot apply. However, it is possible that nonequilibrium steady states may have a thermodynamics description. We explore the [...] Read more.
The concepts of temperature and entropy as applied in equilibrium thermodynamics do not easily generalize to nonequilibrium systems and there are transient systems where thermodynamics cannot apply. However, it is possible that nonequilibrium steady states may have a thermodynamics description. We explore the consequences of a particular microscopic thermostat-reservoir contact needed to both stabilize and measure the temperature of a system. One particular mechanical connection mechanism is considered in detail and a contact resistance is observed in the numerical simulations. We propose a microscopic mechanism to explain this effect for both equilibrium and nonequilibrium systems. These results emphasize the difficulty in identifying a microscopic expression for the thermodynamic temperature. It is evident that the kinetic temperature is not necessarily equal to the thermodynamic temperature, especially when used to define the local temperature. Full article
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Article
Generalized Measure of Departure from No Three-Factor Interaction Model for 2 x 2 x K Contingency Tables
Entropy 2008, 10(4), 776-785; https://doi.org/10.3390/e10040776 - 22 Dec 2008
Viewed by 4777
Abstract
For 2 x 2 x K contingency tables, Tomizawa considered a Shannon entropy type measure to represent the degree of departure from a log-linear model of no three-factor interaction (the NOTFI model). This paper proposes a generalization of Tomizawa's measure for 2 x [...] Read more.
For 2 x 2 x K contingency tables, Tomizawa considered a Shannon entropy type measure to represent the degree of departure from a log-linear model of no three-factor interaction (the NOTFI model). This paper proposes a generalization of Tomizawa's measure for 2 x 2 x K tables. The measure proposed is expressed by using Patil-Taillie diversity index or Cressie-Read power-divergence. A special case of the proposed measure includes Tomizawa's measure. The proposed measure would be useful for comparing the degrees of departure from the NOTFI model in several tables. Full article
(This article belongs to the Special Issue Information and Entropy)
Article
Non-linear Information Inequalities
Entropy 2008, 10(4), 765-775; https://doi.org/10.3390/e10040765 - 22 Dec 2008
Cited by 6 | Viewed by 4329
Abstract
We construct non-linear information inequalities from Mat´uˇs’ infinite series of linear information inequalities. Each single non-linear inequality is sufficiently strong to prove that the closure of the set of all entropy functions is not polyhedral for four or more random variables, a fact [...] Read more.
We construct non-linear information inequalities from Mat´uˇs’ infinite series of linear information inequalities. Each single non-linear inequality is sufficiently strong to prove that the closure of the set of all entropy functions is not polyhedral for four or more random variables, a fact that was already established using the series of linear inequalities. To the best of our knowledge, they are the first non-trivial examples of non-linear information inequalities. Full article
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Article
Speed-gradient Entropy Principle for Nonstationary Processes
Entropy 2008, 10(4), 757-764; https://doi.org/10.3390/e10040757 - 08 Dec 2008
Cited by 15 | Viewed by 4889
Abstract
The speed-gradient variational principle (SG-principle) for nonstationary far from equilibrium systems is formulated and illustrated by examples. The SG-model of transient (relaxation) dynamics for systems of a finite number of particles based on maximum entropy principle is derived. It has the form dX(t)/dt [...] Read more.
The speed-gradient variational principle (SG-principle) for nonstationary far from equilibrium systems is formulated and illustrated by examples. The SG-model of transient (relaxation) dynamics for systems of a finite number of particles based on maximum entropy principle is derived. It has the form dX(t)/dt = AlnX(t); where X(t) is the vector of the cell populations, A is a symmetric matrix with two zero eigenvalues corresponding to mass and energy conservation laws. Full article
Article
An Assessment of Hermite Function Based Approximations of Mutual Information Applied to Independent Component Analysis
Entropy 2008, 10(4), 745-756; https://doi.org/10.3390/e10040745 - 04 Dec 2008
Cited by 4 | Viewed by 6797
Abstract
At the heart of many ICA techniques is a nonparametric estimate of an information measure, usually via nonparametric density estimation, for example, kernel density estimation. While not as popular as kernel density estimators, orthogonal functions can be used for nonparametric density estimation (via [...] Read more.
At the heart of many ICA techniques is a nonparametric estimate of an information measure, usually via nonparametric density estimation, for example, kernel density estimation. While not as popular as kernel density estimators, orthogonal functions can be used for nonparametric density estimation (via a truncated series expansion whose coefficients are calculated from the observed data). While such estimators do not necessarily yield a valid density, which kernel density estimators do, they are faster to calculate than kernel density estimators, in particular for a modified version of Renyi's entropy of order 2. In this paper, we compare the performance of ICA using Hermite series based estimates of Shannon's and Renyi's mutual information, to that of Gaussian kernel based estimates. The comparisons also include ICA using the RADICAL estimate of Shannon's entropy and a FastICA estimate of neg-entropy. Full article
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Article
Information Entropy of Influenza A Segment 7
Entropy 2008, 10(4), 736-744; https://doi.org/10.3390/e10040736 - 23 Nov 2008
Cited by 2 | Viewed by 5613
Abstract
Information entropy (H) is a measure of uncertainty at each position within in a sequence of nucleotides.H was used to characterize a set of influenza A segment 7 nucleotide sequences. Nucleotide locations of high entropy were identified near the 5’ start of all [...] Read more.
Information entropy (H) is a measure of uncertainty at each position within in a sequence of nucleotides.H was used to characterize a set of influenza A segment 7 nucleotide sequences. Nucleotide locations of high entropy were identified near the 5’ start of all of the sequences and the sequences were assigned to subsets according to synonymous nucleotide variants at those positions: either uracil at position six (U6), cytosine at position six (C6), adenine (A12) at position 12, guanine at position 12 (G12), adenine at position 15 (A15) or cytosine (C15) at position 15. H values were found to be correlated/corresponding (Kendall tau) along the lengths of the nucleotide segments of the subset pairs at each position. However, the H values of each subset of sequences were statistically distinguishable from those of the other member of the pair (Kolmogorov-Smirnov test). The joint probability of uncorrelated distributions of U6 and C6 sequences to viral subtypes and to viral host species was 34 times greater than for the A12:G12 subset pair and 214 times greater than for the A15:C15 pair. This result indicates that the high entropy position six of segment 7 is either a reporter or a sentinel location. The fact that not one of the H5N1 sequences in the dataset was a member of the C6 subset, but all 125 H5N1 sequences are members of the U6 subset suggests a non-random sentinel function. Full article
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Article
Intercept Capacity: Unknown Unitary Transformation
Entropy 2008, 10(4), 722-735; https://doi.org/10.3390/e10040722 - 20 Nov 2008
Cited by 1 | Viewed by 5176
Abstract
We consider the problem of intercepting communications signals between Multiple-Input Multiple-Output (MIMO) communication systems. To correctly detect a transmitted message it is necessary to know the gain matrix that represents the channel between the transmitter and the receiver. However, even if the receiver [...] Read more.
We consider the problem of intercepting communications signals between Multiple-Input Multiple-Output (MIMO) communication systems. To correctly detect a transmitted message it is necessary to know the gain matrix that represents the channel between the transmitter and the receiver. However, even if the receiver has knowledge of the message symbol set, it may not be possible to estimate the channel matrix. Blind Source Separation (BSS) techniques, such as Independent Component Analysis (ICA) can go some way to extracting independent signals from individual transmission antennae but these may have been preprocessed in a manner unknown to the receiver. In this paper we consider the situation where a communications interception system has prior knowledge of the message symbol set, the channel matrix between the transmission system and the interception system and is able to resolve the transmissionss from independent antennae. The question then becomes: what is the mutual information available to the interceptor when an unknown unitary transformation matrix is employed by the transmitter. Full article
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Article
Comparison of Statistical Dynamical, Square Root and Ensemble Kalman Filters
Entropy 2008, 10(4), 684-721; https://doi.org/10.3390/e10040684 - 20 Nov 2008
Cited by 21 | Viewed by 5395
Abstract
We present a statistical dynamical Kalman filter and compare its performance to deterministic ensemble square root and stochastic ensemble Kalman filters for error covariance modeling with applications to data assimilation. Our studies compare assimilation and error growth in barotropic flows during a period [...] Read more.
We present a statistical dynamical Kalman filter and compare its performance to deterministic ensemble square root and stochastic ensemble Kalman filters for error covariance modeling with applications to data assimilation. Our studies compare assimilation and error growth in barotropic flows during a period in 1979 in which several large scale atmospheric blocking regime transitions occurred in the Northern Hemisphere. We examine the role of sampling error and its effect on estimating the flow dependent growing error structures and the associated effects on the respective Kalman gains. We also introduce a Shannon entropy reduction measure and relate it to the spectra of the Kalman gain. Full article
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Article
Entropy, Closures and Subgrid Modeling
Entropy 2008, 10(4), 635-683; https://doi.org/10.3390/e10040635 - 17 Nov 2008
Cited by 36 | Viewed by 5524
Abstract
Maximum entropy states or statistical mechanical equilibrium solutions have played an important role in the development of a fundamental understanding of turbulence and its role in geophysical flows. In modern general circulation models of the earth’s atmosphere and oceans most parameterizations of the [...] Read more.
Maximum entropy states or statistical mechanical equilibrium solutions have played an important role in the development of a fundamental understanding of turbulence and its role in geophysical flows. In modern general circulation models of the earth’s atmosphere and oceans most parameterizations of the subgrid-scale energy and enstrophy transfers are based on ad hoc methods or ideas developed from equilibrium statistical mechanics or entropy production hypotheses. In this paper we review recent developments in nonequilibrium statistical dynamical closure theory, its application to subgrid-scale modeling of eddy-eddy, eddy-mean field and eddy-topographic interactions and the relationship to minimum enstrophy, maximum entropy and entropy production arguments. Full article
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Article
Relaxed Plasma Equilibria and Entropy-Related Plasma Self-Organization Principles
Entropy 2008, 10(4), 621-634; https://doi.org/10.3390/e10040621 - 14 Nov 2008
Cited by 31 | Viewed by 6245
Abstract
The concept of plasma relaxation as a constrained energy minimization is reviewed. Recent work by the authors on generalizing this approach to partially relaxed threedimensional plasma systems in a way consistent with chaos theory is discussed, with a view to clarifying the thermodynamic [...] Read more.
The concept of plasma relaxation as a constrained energy minimization is reviewed. Recent work by the authors on generalizing this approach to partially relaxed threedimensional plasma systems in a way consistent with chaos theory is discussed, with a view to clarifying the thermodynamic aspects of the variational approach used. Other entropy-related approaches to finding long-time steady states of turbulent or chaotic plasma systems are also briefly reviewed. Full article
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Article
Hurricane Footprints in Global Climate Models
Entropy 2008, 10(4), 613-620; https://doi.org/10.3390/e10040613 - 13 Nov 2008
Cited by 2 | Viewed by 7579
Abstract
This paper addresses the identification of hurricanes in low-resolution global climate models (GCM). As hurricanes are not fully resolvable at the coarse resolution of the GCMs (typically 2.5 × 2.5 deg), indirect methods such as analyzing the environmental conditions favoring hurricane formation have [...] Read more.
This paper addresses the identification of hurricanes in low-resolution global climate models (GCM). As hurricanes are not fully resolvable at the coarse resolution of the GCMs (typically 2.5 × 2.5 deg), indirect methods such as analyzing the environmental conditions favoring hurricane formation have to be sought. Nonetheless, the dynamical cores of the models have limitations in simulating hurricane formation, which is a far from fully understood process. Here, it is shown that variations in the specific entropy rather than in dynamical variables can be used as a proxy of the hurricane intensity as estimated by the Accumulated Cyclone Energy (ACE). The main application of this research is to ascertain the changes in the hurricane frequency and intensity in future climates. Full article
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Article
On the Entropy and Letter Frequencies of Powerfree Words
Entropy 2008, 10(4), 590-612; https://doi.org/10.3390/e10040590 - 12 Nov 2008
Cited by 2 | Viewed by 5428
Abstract
We review the recent progress in the investigation of powerfree words, with particular emphasis on binary cubefree and ternary squarefree words. Besides various bounds on the entropy, we provide bounds on letter frequencies and consider their empirical distribution obtained by an enumeration of [...] Read more.
We review the recent progress in the investigation of powerfree words, with particular emphasis on binary cubefree and ternary squarefree words. Besides various bounds on the entropy, we provide bounds on letter frequencies and consider their empirical distribution obtained by an enumeration of binary cubefree words up to length 80. Full article
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Correction
Entropy 2008, 10, 240-247: Ferri et al. Deformed Generalization of the Semiclassical Entropy
Entropy 2008, 10(4), 589; https://doi.org/10.3390/e10040589 - 11 Nov 2008
Viewed by 5701
Abstract
It has come to our attention that names of authors have been misspelled in a paper recently published in Entropy [1]. The correct names are: Gustavo Ferri, Felipe Olivares, Flavia Pennini, Angelo Plastino, Angel R. Plastino and Montserrat Casas. We apologize for this [...] Read more.
It has come to our attention that names of authors have been misspelled in a paper recently published in Entropy [1]. The correct names are: Gustavo Ferri, Felipe Olivares, Flavia Pennini, Angelo Plastino, Angel R. Plastino and Montserrat Casas. We apologize for this mistake and any inconvenience caused. [...] Full article
Article
Informational Entropy of B-ary Trees after a Vertex Cut
Entropy 2008, 10(4), 576-588; https://doi.org/10.3390/e10040576 - 03 Nov 2008
Cited by 3 | Viewed by 4522
Abstract
Together with stars and paths, b-ary trees are one of the most studied acyclic graph structures. As any other structure, a b-ary tree can be seen as containing information. The aim of the present research was to assess through informational entropy the structural [...] Read more.
Together with stars and paths, b-ary trees are one of the most studied acyclic graph structures. As any other structure, a b-ary tree can be seen as containing information. The aim of the present research was to assess through informational entropy the structural information changes in b-ary trees after removal of an arbitrary vertex. Full article
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Article
Assessing the Information Content in Environmental Modelling: A Carbon Cycle Perspective
Entropy 2008, 10(4), 556-575; https://doi.org/10.3390/e10040556 - 03 Nov 2008
Cited by 7 | Viewed by 4355
Abstract
A model represents the way in which information about the world is captured in a form that can be manipulated for application to new situations. However, quantification of `model error' presents formidable challenges. Various inverse problems in carbon cycle modelling are presented as [...] Read more.
A model represents the way in which information about the world is captured in a form that can be manipulated for application to new situations. However, quantification of `model error' presents formidable challenges. Various inverse problems in carbon cycle modelling are presented as illustrations of the issues. A `maximum-entropy' representation of carbon cycle response is used to explore techniques for non-parametric estimation of carbon cycle uncertainty. Full article
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Article
stu Black Holes Unveiled
Entropy 2008, 10(4), 507-555; https://doi.org/10.3390/e10040507 - 17 Oct 2008
Cited by 79 | Viewed by 6449
Abstract
The general solutions of the radial attractor flow equations for extremal black holes, both for non-BPS with non-vanishing central charge Z and for Z = 0, are obtained for the so-called stu model, the minimal rank-3 N = 2 symmetric supergravity in [...] Read more.
The general solutions of the radial attractor flow equations for extremal black holes, both for non-BPS with non-vanishing central charge Z and for Z = 0, are obtained for the so-called stu model, the minimal rank-3 N = 2 symmetric supergravity in d = 4 space-time dimensions. Comparisons with previous results, as well as the fake supergravity (first order) formalism and an analysis of the BPS bound all along the non-BPS attractor flows and of the marginal stability of corresponding D-brane configurations, are given. Full article
(This article belongs to the Special Issue Symmetry and Entropy)
Article
Entropy and Uncertainty
Entropy 2008, 10(4), 493-506; https://doi.org/10.3390/e10040493 - 16 Oct 2008
Cited by 41 | Viewed by 5404
Abstract
We give a survey of the basic statistical ideas underlying the definition of entropy in information theory and their connections with the entropy in the theory of dynamical systems and in statistical mechanics. Full article
Article
Extended Thermodynamics: a Theory of Symmetric Hyperbolic Field Equations
Entropy 2008, 10(4), 477-492; https://doi.org/10.3390/e10040477 - 15 Oct 2008
Cited by 8 | Viewed by 8047
Abstract
Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear first order differential equations. If the constitutive functions are subject to the requirements of the entropy [...] Read more.
Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear first order differential equations. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation provide an explicit example for extended thermodynamics. The theory proves its usefulness and practicality in the successful treatment of light scattering in rarefied gases. This presentation is based upon the book [1] of which the author of this paper is a co-author. For more details about the motivation and exploitation of the basic principles the interested reader is referred to that reference. It would seem that extended thermodynamics is worthy of the attention of mathematicians. It may offer them a non-trivial field of study concerning hyperbolic equations, if ever they get tired of the Burgers equation. Physicists may prefer to appreciate the success of extended thermodynamics in light scattering and to work on the open problems concerning the modification of the Navier-Stokes-Fourier theory in rarefied gases as predicted by extended thermodynamics of 13, 14, and more moments. Full article
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Article
Entropy and Energy, – a Universal Competition
Entropy 2008, 10(4), 462-476; https://doi.org/10.3390/e10040462 - 15 Oct 2008
Cited by 16 | Viewed by 6088
Abstract
When a body approaches equilibrium, energy tends to a minimum and entropy tends to a maximum. Often, or usually, the two tendencies favour different configurations of the body. Thus energy is deterministic in the sense that it favours fixed positions for the atoms, [...] Read more.
When a body approaches equilibrium, energy tends to a minimum and entropy tends to a maximum. Often, or usually, the two tendencies favour different configurations of the body. Thus energy is deterministic in the sense that it favours fixed positions for the atoms, while entropy randomizes the positions. Both may exert considerable forces in the attempt to reach their objectives. Therefore they have to compromise; indeed, under most circumstances it is the available free energy which achieves a minimum. For low temperatures that free energy is energy itself, while for high temperatures it is determined by entropy. Several examples are provided for the roles of energy and entropy as competitors: – Planetary atmospheres; – osmosis; – phase transitions in gases and liquids and in shape memory alloys, and – chemical reactions, viz. the Haber Bosch synthesis of ammonia and photosynthesis. Some historical remarks are strewn through the text to make the reader appreciate the difficulties encountered by the pioneers in understanding the subtlety of the concept of entropy, and in convincing others of the validity and relevance of their arguments. Full article
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Article
Spacetime Foam: From Entropy and Holography to Infinite Statistics and Nonlocality
Entropy 2008, 10(4), 441-461; https://doi.org/10.3390/e10040441 - 14 Oct 2008
Cited by 58 | Viewed by 7202
Abstract
Due to quantum fluctuations, spacetime is foamy on small scales. The degree of foaminess is found to be consistent with holography, a principle prefigured in the physics of black hole entropy. It has bearing on the ultimate accuracies of clocks and measurements and [...] Read more.
Due to quantum fluctuations, spacetime is foamy on small scales. The degree of foaminess is found to be consistent with holography, a principle prefigured in the physics of black hole entropy. It has bearing on the ultimate accuracies of clocks and measurements and the physics of quantum computation. Consistent with existing archived data on active galactic nuclei from the Hubble Space Telescope, the application of the holographic spacetime foam model to cosmology requires the existence of dark energy which, we argue, is composed of an enormous number of inert “particles” of extremely long wavelength. We suggest that these “particles” obey infinite statistics in which all representations of the particle permutation group can occur, and that the nonlocality present in systems obeying infinite statistics may be related to the nonlocality present in holographic theories. We also propose to detect spacetime foam by looking for halos in the images of distant quasars, and argue that it does not modify the GZK cutoff in the ultra-high energy cosmic ray spectrum and its contributions to time-offlight differences of high energy gamma rays from distant GRB are too small to be detectable. Full article
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Article
Entropy Flow and the Evolution of a Storm
Entropy 2008, 10(4), 430-440; https://doi.org/10.3390/e10040430 - 13 Oct 2008
Cited by 1 | Viewed by 4684
Abstract
The universal principle that an open system can be driven to a state far from equilibrium, or organized, by strong negative entropy flow from its surroundings has been validated in numerous fields from physics and chemistry to the life science. In this paper, [...] Read more.
The universal principle that an open system can be driven to a state far from equilibrium, or organized, by strong negative entropy flow from its surroundings has been validated in numerous fields from physics and chemistry to the life science. In this paper, entropy flows for a severe storm are calculated via the entropy flow formula using the National Centers for Environmental Prediction/National Center for Atmospheric Research reanalysis data. The results show that the intensification of negative (positive) entropy flow entering into the storm preceded the strengthening (weakening) of its intensity, implying that entropy flow analysis can be used as a potential tool in forecasting changes in the intensity of a storm. Full article
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Article
Electromagnetic Nanoscale Metrology Based on Entropy Production and Fluctuations
Entropy 2008, 10(4), 411-429; https://doi.org/10.3390/e10040411 - 08 Oct 2008
Cited by 4 | Viewed by 4991
Abstract
The goal in this paper is to show how many high-frequency electromagnetic metrology areas can be understood and formulated in terms of entropy evolution, production, and fluctuations. This may be important in nanotechnology where an understanding of fluctuations of thermal and electromagnetic energy [...] Read more.
The goal in this paper is to show how many high-frequency electromagnetic metrology areas can be understood and formulated in terms of entropy evolution, production, and fluctuations. This may be important in nanotechnology where an understanding of fluctuations of thermal and electromagnetic energy and the effects of nonequilibrium are particularly important. The approach used here is based on a new derivation of an entropy evolution equation using an exact Liouville-based statistical-mechanical theory rooted in the Robertson-Zwanzig-Mori formulations. The analysis begins by developing an exact equation for entropy rate in terms of time correlations of the microscopic entropy rate. This equation is an exact fluctuation-dissipation relationship. We then define the entropy and its production for electromagnetic driving, both in the time and frequency domains, and apply this to study dielectric and magnetic material measurements, magnetic relaxation, cavity resonance, noise, measuring Boltzmann’s constant, and power measurements. Full article
Article
Configurational Information as Potentially Negative Entropy: The Triple Helix Model
Entropy 2008, 10(4), 391-410; https://doi.org/10.3390/e10040391 - 06 Oct 2008
Cited by 12 | Viewed by 8410
Abstract
Configurational information is generated when three or more sources of variance interact. The variations not only disturb each other relationally, but by selecting upon each other, they are also positioned in a configuration. A configuration can be stabilized and/or globalized. Different stabilizations can [...] Read more.
Configurational information is generated when three or more sources of variance interact. The variations not only disturb each other relationally, but by selecting upon each other, they are also positioned in a configuration. A configuration can be stabilized and/or globalized. Different stabilizations can be considered as second-order variation, and globalization as a second-order selection. The positive manifestations and the negative selections operate upon one another by adding and reducing uncertainty, respectively. Reduction of uncertainty in a configuration can be measured in bits of information. The variables can also be considered as dimensions of the probabilistic entropy in the system(s) under study. The configurational information then provides us with a measure of synergy within a complex system. For example, the knowledge base of an economy can be considered as such a synergy in the otherwise virtual (that is, fourth) dimension of a regime Full article
(This article belongs to the Special Issue Configurational Entropy)
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