Entropy

293 KiB

Open AccessReview

General Framework of Pressure Effects on Structures Formed by Entropically Driven Self-Assembly

by Takashi Yoshidome

Entropy 2010, 12(6), 1632-1652; https://doi.org/10.3390/e12061632 - 23 Jun 2010

Cited by 4 | Viewed by 6896

We review a general framework of pressure effects on the structures formed by entropically driven self-assembly (for example, denaturation of proteins from their native structure and dissociation of ordered structure of the amyloid fibril occur at high pressures). In the framework, the translational [...] Read more.

We review a general framework of pressure effects on the structures formed by entropically driven self-assembly (for example, denaturation of proteins from their native structure and dissociation of ordered structure of the amyloid fibril occur at high pressures). In the framework, the translational entropy of water is an essential factor. Our findings are as follows: at low pressures, the structures almost minimizing the excluded volume (EV) generated for water molecules are stable. On the other hand, at high pressures, the structures possessing the largest possible water-accessible surface area together with sufficiently small EV become more stable. These characteristics are consistent with experimental observations. Full article

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Schematic representation of three side chains. The excluded volume generated by a side chain is the volume occupied by the side chain itself plus the volume shown in gray. When side chains are closely packed, the excluded volumes overlap, leading to a gain of the water entropy. Full article ">Figure 2
Reduced density profiles of hard-sphere solvent near a hard-sphere solute gUS(r) at ρSdS3 = 0.2 (dotted line), ρSdS3 = 0.5 (2-dot dashed line), and ρSdS3 = 0.7 (solid line). Full article ">Figure 3
(a) C1 (Å−3), C2 (Å−2), and C2/C1 (Å) of solvation entropy, −S/kB, plotted against solvent density corresponding to the pressure. (b) C1 and C2 (Å) of partial molar volume plotted against solvent density. Full article ">Figure 4
Negative of the entropy change of solvent scaled by kB upon the transition from the native structure to (a) the swelling structure and (b) the random-coil structures of protein G plotted against the bulk solvent density corresponding to the pressure P. −ΔS/kB = (−S/kB)Unfold−{(−S/kB)Native} where the superscripts “Native” and “Unfold” represent the values for the native structure and for the unfolded structure, respectively. (c) Decomposition of −ΔS/kB for swelling structure of protein G [<a href="#entropy-12-01632-f004" class="html-fig">Figure 4</a>(a)] into C1ΔVex, C2ΔA, and C3ΔX+C4ΔY at each bulk solvent density. Full article ">Figure 5
ΔS and |ΔSC| plotted against the bulk solvent density corresponding to the pressure. |ΔSC| lies between the two dashed lines. The SE gain and the CE loss upon the transition from the coil state (an ensemble of random coils) to the complete α-helix structure are compared. Full article ">

676 KiB

Open AccessArticle

Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels

by Benoît Collins and Ion Nechita

Entropy 2010, 12(6), 1612-1631; https://doi.org/10.3390/e12061612 - 23 Jun 2010

Cited by 9 | Viewed by 7510

Abstract

Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models of relevance for the recent counterexamples to the minimum [...] Read more.

Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models of relevance for the recent counterexamples to the minimum output entropy additivity problems. Our main result is a classification of regimes for which the von Neumann entropy is lower on average than the elementary bounds that can be obtained with linear algebra techniques. Full article

(This article belongs to the Collection Quantum Information)

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877 KiB

Open AccessArticle

Projection Pursuit Through ϕ-Divergence Minimisation

by Jacques Touboul

Entropy 2010, 12(6), 1581-1611; https://doi.org/10.3390/e12061581 - 14 Jun 2010

Cited by 3 | Viewed by 8246

Abstract

In his 1985 article (“Projection pursuit”), Huber demonstrates the interest of his method to estimate a density from a data set in a simple given case. He considers the factorization of density through a Gaussian component and some residual density. Huber’s work is [...] Read more.

In his 1985 article (“Projection pursuit”), Huber demonstrates the interest of his method to estimate a density from a data set in a simple given case. He considers the factorization of density through a Gaussian component and some residual density. Huber’s work is based on maximizing Kullback–Leibler divergence. Our proposal leads to a new algorithm. Furthermore, we will also consider the case when the density to be factorized is estimated from an i.i.d. sample. We will then propose a test for the factorization of the estimated density. Applications include a new test of fit pertaining to the elliptical copulas. Full article

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Graph of the distribution to estimate (red) and of our own estimate (green). Full article ">Figure 2
Graph of the distribution to estimate (red) and of Huber’s estimate (green). Full article ">Figure 3
Graph of the regression of <math display="inline"> <msub> <mi>X</mi> <mn>1</mn> </msub> </math> on <math display="inline"> <msub> <mi>X</mi> <mn>0</mn> </msub> </math> based on the least squares method (red) and based on our theory (green). Full article ">Figure 4
Graph of the regression of <math display="inline"> <msub> <mi>X</mi> <mn>1</mn> </msub> </math> on <math display="inline"> <msub> <mi>X</mi> <mn>0</mn> </msub> </math> based on our theory (green). Full article ">Figure 5
Graph of the estimate of <math display="inline"> <mrow> <mrow> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo stretchy="false">)</mo> </mrow> <mo>↦</mo> <msub> <mi>c</mi> <mi>ρ</mi> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi>F</mi> <mrow> <mi>G</mi> <mi>u</mi> <mi>m</mi> <mi>b</mi> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <msub> <mi>F</mi> <mrow> <mi>E</mi> <mi>x</mi> <mi>p</mi> <mi>o</mi> <mi>n</mi> <mi>e</mi> <mi>n</mi> <mi>t</mi> <mi>i</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math>. Full article ">Figure 6
Graph of the regression of log of Nokia on Sanofi based on the least squares method (red) and based on our theory (green). Full article ">

172 KiB

Open AccessArticle

A Concentrated, Nonlinear Information-Theoretic Estimator for the Sample Selection Model

by Amos Golan and Henryk Gzyl

Entropy 2010, 12(6), 1569-1580; https://doi.org/10.3390/e12061569 - 14 Jun 2010

Viewed by 6734

Abstract

This paper develops a semi-parametric, Information-Theoretic method for estimating parameters for nonlinear data generated under a sample selection process. Considering the sample selection as a set of inequalities makes this model inherently nonlinear. This estimator (i) allows for a whole class of different [...] Read more.

This paper develops a semi-parametric, Information-Theoretic method for estimating parameters for nonlinear data generated under a sample selection process. Considering the sample selection as a set of inequalities makes this model inherently nonlinear. This estimator (i) allows for a whole class of different priors, and (ii) is constructed as an unconstrained, concentrated model. This estimator is easy to apply and works well with small or complex data. We provide a number of explicit analytical examples for different priors’ structures and an empirical example. Full article

523 KiB

Open AccessArticle

Families of Alpha- Beta- and Gamma- Divergences: Flexible and Robust Measures of Similarities

by Andrzej Cichocki and Shun-ichi Amari

Entropy 2010, 12(6), 1532-1568; https://doi.org/10.3390/e12061532 - 14 Jun 2010

Cited by 315 | Viewed by 18003

Abstract

In this paper, we extend and overview wide families of Alpha-, Beta- and Gamma-divergences and discuss their fundamental properties. In literature usually only one single asymmetric (Alpha, Beta or Gamma) divergence is considered. We show in this paper that there exist families of [...] Read more.

In this paper, we extend and overview wide families of Alpha-, Beta- and Gamma-divergences and discuss their fundamental properties. In literature usually only one single asymmetric (Alpha, Beta or Gamma) divergence is considered. We show in this paper that there exist families of such divergences with the same consistent properties. Moreover, we establish links and correspondences among these divergences by applying suitable nonlinear transformations. For example, we can generate the Beta-divergences directly from Alpha-divergences and vice versa. Furthermore, we show that a new wide class of Gamma-divergences can be generated not only from the family of Beta-divergences but also from a family of Alpha-divergences. The paper bridges these divergences and shows also their links to Tsallis and Rényi entropies. Most of these divergences have a natural information theoretic interpretation. Full article

718 KiB

Open AccessCommunication

Fairness Is an Emergent Self-Organized Property of the Free Market for Labor

by Venkat Venkatasubramanian

Entropy 2010, 12(6), 1514-1531; https://doi.org/10.3390/e12061514 - 14 Jun 2010

Cited by 12 | Viewed by 16740

Abstract

The excessive compensation packages of CEOs of U.S. corporations in recent years have brought to the foreground the issue of fairness in economics. The conventional wisdom is that the free market for labor, which determines the pay packages, cares only about efficiency and [...] Read more.

The excessive compensation packages of CEOs of U.S. corporations in recent years have brought to the foreground the issue of fairness in economics. The conventional wisdom is that the free market for labor, which determines the pay packages, cares only about efficiency and not fairness. We present an alternative theory that shows that an ideal free market environment also promotes fairness, as an emergent property resulting from the self-organizing market dynamics. Even though an individual employee may care only about his or her salary and no one else’s, the collective actions of all the employees, combined with the profit maximizing actions of all the companies, in a free market environment under budgetary constraints, lead towards a more fair allocation of wages, guided by Adam Smith’s invisible hand of self-organization. By exploring deep connections with statistical thermodynamics, we show that entropy is the appropriate measure of fairness in a free market environment which is maximized at equilibrium to yield the lognormal distribution of salaries as the fairest inequality of pay in an organization under ideal conditions. Full article

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392 KiB

Open AccessArticle

Entropy-Based Method of Choosing the Decomposition Level in Wavelet Threshold De-noising

by Yan-Fang Sang, Dong Wang and Ji-Chun Wu

Entropy 2010, 12(6), 1499-1513; https://doi.org/10.3390/e12061499 - 10 Jun 2010

Cited by 45 | Viewed by 8812

Abstract

In this paper, the energy distributions of various noises following normal, log-normal and Pearson-III distributions are first described quantitatively using the wavelet energy entropy (WEE), and the results are compared and discussed. Then, on the basis of these analytic results, a method for [...] Read more.

In this paper, the energy distributions of various noises following normal, log-normal and Pearson-III distributions are first described quantitatively using the wavelet energy entropy (WEE), and the results are compared and discussed. Then, on the basis of these analytic results, a method for use in choosing the decomposition level (DL) in wavelet threshold de-noising (WTD) is put forward. Finally, the performance of the proposed method is verified by analysis of both synthetic and observed series. Analytic results indicate that the proposed method is easy to operate and suitable for various signals. Moreover, contrary to traditional white noise testing which depends on “autocorrelations”, the proposed method uses energy distributions to distinguish real signals and noise in noisy series, therefore the chosen DL is reliable, and the WTD results of time series can be improved. Full article

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480 KiB

Open AccessArticle

Prediction of Droplet Size and Velocity Distribution in Droplet Formation Region of Liquid Spray

by Ehsan Movahednejad, Fathollah Ommi and S. Mostafa Hosseinalipour

Entropy 2010, 12(6), 1484-1498; https://doi.org/10.3390/e12061484 - 10 Jun 2010

Cited by 43 | Viewed by 11495

Abstract

Determining the distributions of size and velocity of droplets formed at the end of primary breakup region is followed in this paper. The droplet formation stage at the end of primary breakup is random and stochastic and it can be modeled by statistical [...] Read more.

Determining the distributions of size and velocity of droplets formed at the end of primary breakup region is followed in this paper. The droplet formation stage at the end of primary breakup is random and stochastic and it can be modeled by statistical means based on the maximum entropy principle (MEP). The MEP formulation predicts the atomization process while satisfying constraint equations based on conservations of mass, momentum and energy. This model is capable of considering drag force on produced droplets through gas-liquid interaction using new approach. The model prediction is compared favorably with the experimentally measured size and velocity distributions of droplets for sprays produced by the two nozzles of considerably different geometries and shows satisfactory agreement. Full article

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Comparison of theoretical and experimental contour. Full article ">Figure 2
Comparison of theoretical (solid line) and experimental (dashed line) [<a href="#B12-entropy-12-01484" class="html-bibr">12</a>] droplet size distribution. Full article ">Figure 3
Comparison between the theoretical (MEP) and experimental (Mitra [<a href="#B18-entropy-12-01484" class="html-bibr">18</a>]) droplet size distribution for PWC nozzle. Full article ">Figure 4
Atomization regions of the spray from the hollow cone nozzle [<a href="#B22-entropy-12-01484" class="html-bibr">22</a>]. Full article ">Figure 5
Number density of droplets versus dimensionless droplet size. Full article ">Figure 6
Number density of droplets versus dimensionless droplet velocity. Full article ">Figure 7
Droplet size distribution of PWC nozzle for two different positions in downstream direction [<a href="#B18-entropy-12-01484" class="html-bibr">18</a>]. Full article ">Figure 8
Prediction of droplet size distribution of PWC nozzle using MEP model for two different positions in downstream direction. Full article ">

2596 KiB

Open AccessArticle

A Network Model of Interpersonal Alignment in Dialog

by Alexander Mehler, Andy Lücking and Petra Weiß

Entropy 2010, 12(6), 1440-1483; https://doi.org/10.3390/e12061440 - 9 Jun 2010

Cited by 49 | Viewed by 10202

Abstract

In dyadic communication, both interlocutors adapt to each other linguistically, that is, they align interpersonally. In this article, we develop a framework for modeling interpersonal alignment in terms of the structural similarity of the interlocutors’ dialog lexica. This is done by means [...] Read more.

In dyadic communication, both interlocutors adapt to each other linguistically, that is, they align interpersonally. In this article, we develop a framework for modeling interpersonal alignment in terms of the structural similarity of the interlocutors’ dialog lexica. This is done by means of so-called two-layer time-aligned network series, that is, a time-adjusted graph model. The graph model is partitioned into two layers, so that the interlocutors’ lexica are captured as subgraphs of an encompassing dialog graph. Each constituent network of the series is updated utterance-wise. Thus, both the inherent bipartition of dyadic conversations and their gradual development are modeled. The notion of alignment is then operationalized within a quantitative model of structure formation based on the mutual information of the subgraphs that represent the interlocutor’s dialog lexica. By adapting and further developing several models of complex network theory, we show that dialog lexica evolve as a novel class of graphs that have not been considered before in the area of complex (linguistic) networks. Additionally, we show that our framework allows for classifying dialogs according to their alignment status. To the best of our knowledge, this is the first approach to measuring alignment in communication that explores the similarities of graph-like cognitive representations. Full article

(This article belongs to the Special Issue Complexity of Human Language and Cognition)

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159 KiB

Open AccessArticle

Thermodynamical Description of Running Discontinuities: Application to Friction and Wear

by Claude Stolz

Entropy 2010, 12(6), 1418-1439; https://doi.org/10.3390/e12061418 - 1 Jun 2010

Cited by 13 | Viewed by 7920

Abstract

The friction and wear phenomena appear due to contact and relative motion between two solids. The evolution of contact conditions depends on loading conditions and mechanical behaviours. The wear phenomena are essentially characterized by a matter loss. Wear and friction are in interaction [...] Read more.

The friction and wear phenomena appear due to contact and relative motion between two solids. The evolution of contact conditions depends on loading conditions and mechanical behaviours. The wear phenomena are essentially characterized by a matter loss. Wear and friction are in interaction due to the fact that particles are detached from the solids. A complex medium appears as an interface having a strong effect on the friction condition. The purpose of this paper is to describe such phenomena taking account of different scales of modelization in order to derive some macroscopic laws. A thermodynamical approach is proposed and models of wear are analysed in this framework where the separation between the dissipation due to friction and that due to wear is made. Applications on different cases are presented. Full article

(This article belongs to the Special Issue Entropy and Friction Volume 2)

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3829 KiB

Open AccessArticle

Effect of an External Oriented Magnetic Field on Entropy Generation in Natural Convection

by Atef El Jery, Nejib Hidouri, Mourad Magherbi and Ammar Ben Brahim

Entropy 2010, 12(6), 1391-1417; https://doi.org/10.3390/e12061391 - 28 May 2010

Cited by 59 | Viewed by 9374

Abstract

The influence of an external oriented magnetic field on entropy generation in natural convection for air and liquid gallium is numerically studied in steady-unsteady states by solving the mass, the momentum and the energy conservation equations. Entropy generation depends on five parameters which [...] Read more.

The influence of an external oriented magnetic field on entropy generation in natural convection for air and liquid gallium is numerically studied in steady-unsteady states by solving the mass, the momentum and the energy conservation equations. Entropy generation depends on five parameters which are: the Prandtl number, the irreversibility coefficients, the inclination angle of the magnetic field, the thermal Grashof and the Hartmann numbers. Effects of these parameters on total and local irreversibilities as well as on heat transfer and fluid flow are studied. It was found that the magnetic field tends to decrease the convection currents, the heat transfer and entropy generation inside the enclosure. Influence of inclination angle of the magnetic field on local irreversibility is then studied. Full article

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964 KiB

Open AccessArticle

Entropy in Tribology: in the Search for Applications

by Michael Nosonovsky

Entropy 2010, 12(6), 1345-1390; https://doi.org/10.3390/e12061345 - 28 May 2010

Cited by 83 | Viewed by 10318

Abstract

The paper discusses the concept of entropy as applied to friction and wear. Friction and wear are classical examples of irreversible dissipative processes, and it is widely recognized that entropy generation is their important quantitative measure. On the other hand, the use of [...] Read more.

The paper discusses the concept of entropy as applied to friction and wear. Friction and wear are classical examples of irreversible dissipative processes, and it is widely recognized that entropy generation is their important quantitative measure. On the other hand, the use of thermodynamic methods in tribology remains controversial and questions about the practical usefulness of these methods are often asked. A significant part of entropic tribological research was conducted in Russia since the 1970s. Surprisingly, many of these studies are not available in English and still not well known in the West. The paper reviews various views on the role of entropy and self-organization in tribology and it discusses modern approaches to wear and friction, which use the thermodynamic entropic method as well as the application of the mathematical concept of entropy to the dynamic friction effects (e.g., the running-in transient process, stick-slip motion, etc.) and a possible connection between the thermodynamic and information approach. The paper also discusses non-equilibrium thermodynamic approach to friction, wear, and self-healing. In general, the objective of this paper is to answer the frequently asked question “is there any practical application of the thermodynamics in the study of friction and wear?” and to show that the thermodynamic methods have potential for both fundamental study of friction and wear and for the development of new (e.g., self-lubricating) materials. Full article

(This article belongs to the Special Issue Entropy and Friction Volume 2)

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64 KiB

Open AccessCorrection

Misleading Reference

by Peter Harremoës

Entropy 2010, 12(6), 1344; https://doi.org/10.3390/e12061344 - 27 May 2010

Viewed by 5458

Abstract

We just became aware that the article [1] published in Entropy 2009 contains a false reference. [...] Full article

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Open AccessArticle

Cultural Naturalism

by Arto Annila and Stanley Salthe

Entropy 2010, 12(6), 1325-1343; https://doi.org/10.3390/e12061325 - 26 May 2010

Cited by 24 | Viewed by 10389

Abstract

Culture can be viewed as the means by which a society can live in its surroundings by acquiring and consuming free energy. This naturalistic notion assumes that everything can be valued in terms of energy, hence also social changes can be described as [...] Read more.

Culture can be viewed as the means by which a society can live in its surroundings by acquiring and consuming free energy. This naturalistic notion assumes that everything can be valued in terms of energy, hence also social changes can be described as natural processes that are influenced by the 2nd Law of Thermodynamics. This universal law, when formulated as an equation of motion, reveals that societies emerge, evolve and eventually extinguish after tapping, exploiting and finally depleting their resources, which we can say are ultimately valued in energetic terms. The analysis reveals that trajectories of societies are, however, inherently non-integrable, i.e., unpredictable in detail because free energy as the driving force, being finite, is inseparable from the flows of energy. Nonetheless, the universal tendency to diminish energy differences within a system and with respect to its surroundings in the least possible time gives rise to highly economical but seemingly immaterial means of energy transduction that associate with cultural codes, habits, traditions, taboos and values. Moreover, cultural naturalism clarifies that identities develop and mature in interactions, and that class structure results from the quest for maximum entropy partition. While social changes in complex societies are inherently intractable, the profound principle allows us to recognize universal tendencies in diverse cultural characteristics, and to rationalize prospects for the future. Full article

(This article belongs to the Special Issue Nonequilibrium Thermodynamics)

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Entropy, Volume 12, Issue 6 (June 2010) – 14 articles , Pages 1325-1652

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