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Entropy, Volume 13, Issue 8 (August 2011) – 6 articles , Pages 1425-1540

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95 KiB

Open AccessCommentary

Distinguishability in Entropy Calculations: Chemical Reactions, Conformational and Residual Entropy

by Ernesto Suárez

Entropy 2011, 13(8), 1533-1540; https://doi.org/10.3390/e13081533 - 23 Aug 2011

Cited by 2 | Viewed by 5697

Abstract

By analyzing different examples of practical entropy calculations and using concepts such as conformational and residual entropies, I show herein that experimental calorimetric entropies of single molecules can be theoretically reproduced considering chemically identical atoms either as distinguishable or indistinguishable particles. The broadly used correction in entropy calculations due to the symmetry number and particle indistinguishability is not mandatory, as an ad hoc correction, to obtain accurate values of absolute and relative entropies. It is shown that, for any chemical reaction of any kind, considering distinguishability or indistinguishability among identical atoms is irrelevant as long as we act consistently in the calculation of all the required entropy contributions. Full article

(This article belongs to the Special Issue Residual and Ground State Entropy)

2392 KiB

Open AccessArticle

A Risk Profile for Information Fusion Algorithms

by Kenric P. Nelson, Brian J. Scannell and Herbert Landau

Entropy 2011, 13(8), 1518-1532; https://doi.org/10.3390/e13081518 - 17 Aug 2011

Cited by 10 | Viewed by 7854

Abstract

E.T. Jaynes, originator of the maximum entropy interpretation of statistical mechanics, emphasized that there is an inevitable trade-off between the conflicting requirements of robustness and accuracy for any inferencing algorithm. This is because robustness requires discarding of information in order to reduce the sensitivity to outliers. The principal of nonlinear statistical coupling, which is an interpretation of the Tsallis entropy generalization, can be used to quantify this trade-off. The coupled-surprisal, -ln_κ(p)≡-(p^κ-1)/κ , is a generalization of Shannon surprisal or the logarithmic scoring rule, given a forecast p of a true event by an inferencing algorithm. The coupling parameter κ=1-q, where q is the Tsallis entropy index, is the degree of nonlinear coupling between statistical states. Positive (negative) values of nonlinear coupling decrease (increase) the surprisal information metric and thereby biases the risk in favor of decisive (robust) algorithms relative to the Shannon surprisal (κ=0). We show that translating the average coupled-surprisal to an effective probability is equivalent to using the generalized mean of the true event probabilities as a scoring rule. The metric is used to assess the robustness, accuracy, and decisiveness of a fusion algorithm. We use a two-parameter fusion algorithm to combine input probabilities from N sources. The generalized mean parameter ‘alpha’ varies the degree of smoothing and raising to a power Ν^β with β between 0 and 1 provides a model of correlation. Full article

(This article belongs to the Special Issue Tsallis Entropy)

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916 KiB

Open AccessReview

Thermodynamics of Thermoelectric Phenomena and Applications

by Christophe Goupil, Wolfgang Seifert, Knud Zabrocki, Eckhart Müller and G. Jeffrey Snyder

Entropy 2011, 13(8), 1481-1517; https://doi.org/10.3390/e13081481 - 15 Aug 2011

Cited by 241 | Viewed by 25772

Abstract

Fifty years ago, the optimization of thermoelectric devices was analyzed by considering the relation between optimal performances and local entropy production. Entropy is produced by the irreversible processes in thermoelectric devices. If these processes could be eliminated, entropy production would be reduced to zero, and the limiting Carnot efficiency or coefficient of performance would be obtained. In the present review, we start with some fundamental thermodynamic considerations relevant for thermoelectrics. Based on a historical overview, we reconsider the interrelation between optimal performances and local entropy production by using the compatibility approach together with the thermodynamic arguments. Using the relative current density and the thermoelectric potential, we show that minimum entropy production can be obtained when the thermoelectric potential is a specific, optimal value. Full article

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8585 KiB

Open AccessArticle

Size of the Whole versus Number of Parts in Genomes

by Antoni Hernández-Fernández, Jaume Baixeries, Núria Forns and Ramon Ferrer-i-Cancho

Entropy 2011, 13(8), 1465-1480; https://doi.org/10.3390/e13081465 - 05 Aug 2011

Cited by 19 | Viewed by 7439

Abstract

It is known that chromosome number tends to decrease as genome size increases in angiosperm plants. Here the relationship between number of parts (the chromosomes) and size of the whole (the genome) is studied for other groups of organisms from different kingdoms. Two major results are obtained. First, the finding of relationships of the kind “the more parts the smaller the whole” as in angiosperms, but also relationships of the kind “the more parts the larger the whole”. Second, these dependencies are not linear in general. The implications of the dependencies between genome size and chromosome number are two-fold. First, they indicate that arguments against the relevance of the finding of negative correlations consistent with Menzerath-Altmann law (a linguistic law that relates the size of the parts with the size of the whole) in genomes are seriously flawed. Second, they unravel the weakness of a recent model of chromosome lengths based upon random breakage that assumes that chromosome number and genome size are independent. Full article

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5658 KiB

Open AccessArticle

Second Law Analysis for Variable Viscosity Hydromagnetic Boundary Layer Flow with Thermal Radiation and Newtonian Heating

by Oluwole Daniel Makinde

Entropy 2011, 13(8), 1446-1464; https://doi.org/10.3390/e13081446 - 05 Aug 2011

Cited by 90 | Viewed by 8254

Abstract

The present paper is concerned with the analysis of inherent irreversibility in hydromagnetic boundary layer flow of variable viscosity fluid over a semi-infinite flat plate under the influence of thermal radiation and Newtonian heating. Using local similarity solution technique and shooting quadrature, the velocity and temperature profiles are obtained numerically and utilized to compute the entropy generation number. The effects of magnetic field parameter, Brinkmann number, the Prandtl number, variable viscosity parameter, radiation parameter and local Biot number on the fluid velocity profiles, temperature profiles, local skin friction and local Nusselt number are presented. The influences of the same parameters and the dimensionless group parameter on the entropy generation rate in the flow regime and Bejan number are calculated, depicted graphically and discussed quantitatively. It is observed that the peak of entropy generation rate is attained within the boundary layer region and plate surface act as a strong source of entropy generation and heat transfer irreversibility. Full article

(This article belongs to the Special Issue Entropy Generation Minimization)

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16407 KiB

Open AccessArticle

A Maximum Entropy Estimator for the Aggregate Hierarchical Logit Model

by Pedro Donoso, Louis De Grange and Felipe González

Entropy 2011, 13(8), 1425-1445; https://doi.org/10.3390/e13081425 - 02 Aug 2011

Cited by 7 | Viewed by 6438

Abstract

A new approach for estimating the aggregate hierarchical logit model is presented. Though usually derived from random utility theory assuming correlated stochastic errors, the model can also be derived as a solution to a maximum entropy problem. Under the latter approach, the Lagrange multipliers of the optimization problem can be understood as parameter estimators of the model. Based on theoretical analysis and Monte Carlo simulations of a transportation demand model, it is demonstrated that the maximum entropy estimators have statistical properties that are superior to classical maximum likelihood estimators, particularly for small or medium-size samples. The simulations also generated reduced bias in the estimates of the subjective value of time and consumer surplus. Full article

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