Entropy

86 KiB

Open AccessArticle

Tsallis Entropy, Escort Probability and the Incomplete Information Theory

by Amir Hossein Darooneh, Ghassem Naeimi, Ali Mehri and Parvin Sadeghi

Entropy 2010, 12(12), 2497-2503; https://doi.org/10.3390/e12122497 - 21 Dec 2010

Cited by 15 | Viewed by 9266

Non-extensive statistical mechanics appears as a powerful way to describe complex systems. Tsallis entropy, the main core of this theory has been remained as an unproven assumption. Many people have tried to derive the Tsallis entropy axiomatically. Here we follow the work of [...] Read more.

Non-extensive statistical mechanics appears as a powerful way to describe complex systems. Tsallis entropy, the main core of this theory has been remained as an unproven assumption. Many people have tried to derive the Tsallis entropy axiomatically. Here we follow the work of Wang (EPJB, 2002) and use the incomplete information theory to retrieve the Tsallis entropy. We change the incomplete information axioms to consider the escort probability and obtain a correct form of Tsallis entropy in comparison with Wang’s work. Full article

(This article belongs to the Special Issue Advances in Statistical Mechanics)

229 KiB

Open AccessArticle

Burning Speed and Entropy Production Calculation of a Transient Expanding Spherical Laminar Flame Using a Thermodynamic Model

by Kian Eisazadeh-Far, Ali Moghaddas, Faranak Rahim and Hameed Metghalchi

Entropy 2010, 12(12), 2485-2496; https://doi.org/10.3390/e12122485 - 21 Dec 2010

Cited by 30 | Viewed by 8263

Abstract

A thermodynamic model has been developed to calculate burning speed and entropy production of transient expending spherical laminar flame in an enclosed vessel. The model also predicts the particle trajectories of both unburned and burned gases in the vessel. The input to this [...] Read more.

A thermodynamic model has been developed to calculate burning speed and entropy production of transient expending spherical laminar flame in an enclosed vessel. The model also predicts the particle trajectories of both unburned and burned gases in the vessel. The input to this model is the dynamic pressure rise due to combustion process. The unburned gases are divided into three regions: The core unburned gases which are compressed isentropically, the vessel walls and electrodes boundary layer gases, and gases in the preheat zone of the flames. The burned gases are in many shells having the same pressure but different temperatures. The model also includes radiation losses from the burned gases to vessel walls. Entropy production due to irreversibility has been calculated by applying entropy balance to the gas mixtures. Burning speed of premixed n-decane air mixture has been reported for temperatures and pressures along an isentrope. Full article

(This article belongs to the Special Issue Advances in Thermodynamics)

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145 KiB

Open AccessArticle

Reconsideration of Criteria and Modeling in Order to Optimize the Efficiency of Irreversible Thermomechanical Heat Engines

by Michel Feidt

Entropy 2010, 12(12), 2470-2484; https://doi.org/10.3390/e12122470 - 21 Dec 2010

Cited by 9 | Viewed by 7082

Abstract

The purpose of this work is to precise and complete one recently proposed in the literature and relative to a general criterion to maximize the first law efficiency of irreversible heat engines. It is shown that the previous proposal seems to be a [...] Read more.

The purpose of this work is to precise and complete one recently proposed in the literature and relative to a general criterion to maximize the first law efficiency of irreversible heat engines. It is shown that the previous proposal seems to be a particular case. A new proposal has been developed for a Carnot irreversible thermomechanical heat engine at steady state associated to two infinite heat reservoirs (hot source, and cold sink): this constitutes the studied system. The presence of heat leak is accounted for, with the most simple form, as is done generally in the literature. Irreversibility is modeled through , created internal entropy rate in the converter (engine), and , total created entropy rate in the system. Heat transfer laws are represented as general functions of temperatures. These concepts are particularized to the most common heat transfer law (linear one). Consequences of the proposal are examined; some new analytical results are proposed for efficiencies. Full article

(This article belongs to the Special Issue Advances in Thermodynamics)

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1467 KiB

Open AccessReview

Using Entropy Leads to a Better Understanding of Biological Systems

by Chih-Yuan Tseng and Jack A. Tuszynski

Entropy 2010, 12(12), 2450-2469; https://doi.org/10.3390/e12122450 - 17 Dec 2010

Cited by 4 | Viewed by 7023

Abstract

In studying biological systems, conventional approaches based on the laws of physics almost always require introducing appropriate approximations. We argue that a comprehensive approach that integrates the laws of physics and principles of inference provides a better conceptual framework than these approaches to [...] Read more.

In studying biological systems, conventional approaches based on the laws of physics almost always require introducing appropriate approximations. We argue that a comprehensive approach that integrates the laws of physics and principles of inference provides a better conceptual framework than these approaches to reveal emergence in such systems. The crux of this comprehensive approach hinges on entropy. Entropy is not merely a physical quantity. It is also a reasoning tool to process information with the least bias. By reviewing three distinctive examples from protein folding dynamics to drug design, we demonstrate the developments and applications of this comprehensive approach in the area of biological systems. Full article

(This article belongs to the Special Issue Emergence in Chemical Systems)

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260 KiB

Open AccessReview

Calculation of the Entropy Balance Equation in a Non-equilibrium Reaction-diffusion System

by Hitoshi Mahara and Tomohiko Yamaguchi

Entropy 2010, 12(12), 2436-2449; https://doi.org/10.3390/e12122436 - 17 Dec 2010

Cited by 7 | Viewed by 9767

Abstract

In this article, we discuss the relationships between thermodynamic quantities and the spatial pattern in a reaction-diffusion model based on the reversible Gray-Scott model. This model is introduced for calculation of the entropy production in a reaction-diffusion system. First, we show the relationship [...] Read more.

In this article, we discuss the relationships between thermodynamic quantities and the spatial pattern in a reaction-diffusion model based on the reversible Gray-Scott model. This model is introduced for calculation of the entropy production in a reaction-diffusion system. First, we show the relationship between entropy production and pattern formation, and suggest that the entropy production could be an index of different patterns. Then the entropy production is applied for searching the parameter region where the pattern is bistable. Moreover, the entropy change is calculated by using the relative chemical potential that is defined based on the equilibrium state and not on the standard chemical potential. The results of the entropy change are consistent with the intrinsic property of the entropy, therefore, the entropy change calculated in this way may be regarded as an appropriate quantity for the discussion of the thermodynamic properties in a non equilibrium system. Full article

(This article belongs to the Section Entropy Reviews)

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163 KiB

Open AccessArticle

Statistical Vibroacoustics and Entropy Concept

by Alain Le Bot, Antonio Carcaterra and Denis Mazuyer

Entropy 2010, 12(12), 2418-2435; https://doi.org/10.3390/e12122418 - 13 Dec 2010

Cited by 25 | Viewed by 7994

Abstract

Statistical vibroacoustics, also called statistical energy analysis (SEA) in the field of engineering, is born from the application of statistical physics concepts to the study of random vibration in mechanical and acoustical systems. This article is a discussion on the thermodynamic foundation for [...] Read more.

Statistical vibroacoustics, also called statistical energy analysis (SEA) in the field of engineering, is born from the application of statistical physics concepts to the study of random vibration in mechanical and acoustical systems. This article is a discussion on the thermodynamic foundation for that approach with particular emphasis devoted to the meaning of entropy, a concept missing in SEA. The theory focuses on vibration confined to the audio frequency range. In this frequency band, heat is defined as random vibration that is disordered vibration and temperature is the vibration energy per mode. Always in this frequency band, the concept of entropy is introduced and its meaning and role in vibroacoustics are enlightened, together with the related evolutionary equation. It is shown that statistical vibroacoustics is non-equilibrium thermodynamics applied to the audio range. Full article

(This article belongs to the Special Issue Nonequilibrium Thermodynamics)

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236 KiB

Open AccessArticle

Forecasting the Stock Market with Linguistic Rules Generated from the Minimize Entropy Principle and the Cumulative Probability Distribution Approaches

by Chung-Ho Su, Tai-Liang Chen, Ching-Hsue Cheng and Ya-Ching Chen

Entropy 2010, 12(12), 2397-2417; https://doi.org/10.3390/e12122397 - 3 Dec 2010

Cited by 16 | Viewed by 8657

Abstract

To forecast a complex and non-linear system, such as a stock market, advanced artificial intelligence algorithms, like neural networks (NNs) and genetic algorithms (GAs) have been proposed as new approaches. However, for the average stock investor, two major disadvantages are argued against these [...] Read more.

To forecast a complex and non-linear system, such as a stock market, advanced artificial intelligence algorithms, like neural networks (NNs) and genetic algorithms (GAs) have been proposed as new approaches. However, for the average stock investor, two major disadvantages are argued against these advanced algorithms: (1) the rules generated by NNs and GAs are difficult to apply in investment decisions; and (2) the time complexity of the algorithms to produce forecasting outcomes is very high. Therefore, to provide understandable rules for investors and to reduce the time complexity of forecasting algorithms, this paper proposes a novel model for the forecasting process, which combines two granulating methods (the minimize entropy principle approach and the cumulative probability distribution approach) and a rough set algorithm. The model verification demonstrates that the proposed model surpasses the three listed conventional fuzzy time-series models and a multiple regression model (MLR) in forecast accuracy. Full article

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280 KiB

Open AccessArticle

Uncertainty Analysis of Decomposition Level Choice in Wavelet Threshold De-Noising

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

Entropy 2010, 12(12), 2386-2396; https://doi.org/10.3390/e12122386 - 30 Nov 2010

Cited by 6 | Viewed by 7069

Abstract

In this paper, the complexities of various noises, which are quantified by wavelet energy entropy (WEE) and differential coefficient of WEE (D(WEE)), were first analyzed and their uncertainties then estimated and described using confidence intervals. Then, quantitative criterion for judging the WEE and [...] Read more.

In this paper, the complexities of various noises, which are quantified by wavelet energy entropy (WEE) and differential coefficient of WEE (D(WEE)), were first analyzed and their uncertainties then estimated and described using confidence intervals. Then, quantitative criterion for judging the WEE and D(WEE) difference between noisy series and noise was put forward, based on which the decomposition level (DL) choice method in wavelet threshold de-noising proposed in 2010 by Sang et al. was improved. Finally, analytical results from examples verified the performance of the improved method, and also demonstrated its much wider applicability; moreover, the DL chosen using it is more reliable because of the fact that uncertainty is taken into consideration. Full article

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217 KiB

Open AccessArticle

Bioentropy, Aesthetics and Meta-dualism: The Transdisciplinary Ecology of Gregory Bateson

by Peter Harries-Jones

Entropy 2010, 12(12), 2359-2385; https://doi.org/10.3390/e12122359 - 26 Nov 2010

Cited by 8 | Viewed by 14329

Abstract

In this paper I am going to be dealing with Gregory Bateson, a theorist who is one of the founders of cybernetics, an acknowledged precursor of Biosemiotics, and in all respects highly transdisciplinary. Until his entry into cybernetics Bateson was an anthropologist and [...] Read more.

In this paper I am going to be dealing with Gregory Bateson, a theorist who is one of the founders of cybernetics, an acknowledged precursor of Biosemiotics, and in all respects highly transdisciplinary. Until his entry into cybernetics Bateson was an anthropologist and like anthropologists of his day, accepted a semantic approach to meaning through the classic work of Ogden and Richards and their thought-word-meaning triangle. Ogden and Richards developed their semantic triangle from Peirce, but effectively turned the Peircian semiotic triad into a pentad of addressors and addressees, to which Bateson added context and reflexivity through feedback loops. The emergence of cybernetics and information theory in the 1940s increased the salience of the notion of feedback yet, he argued, information theory had truncated the notion of meaning. Bateson’s discussion of the logical categories of learning and communication distinguished the difference between and ‘sign’ and ‘signal’. Cybernetic signaling was a form of zero‑learning; living systems were interpretative and engaged in several logical types of learning. Twenty years later he took up similar sorts of issues with regard to the new science of ecology which had framed systemic ‘entropy’ solely in thermodynamic terms and ignored communication and learning in living systems. His concept of Bioentropy is presented in section two of this paper as is its association with redundancy. Bioentropy, in turn, led to his offering an entirely new definition of information: “the difference that makes a difference.” The definition could apply to both human and non-human communication patterns, since some forms of animal communication could not undertake logical typing. Finally, he believed that his own systemic approach was insufficient for meta-dualism. He promoted the idea of an ecological aesthetics which needed to be sufficiently objective to deal with the many disruptions in its own recursive relations, yet subjective and self-reflexive in the manner of a creative epistemology. ‘Rigor’ and ‘imagination’ became Bateson’s meta-logical types and aesthetics his meta-dualism. He drew his inspiration from the aesthetics of R.G. Collingwood. By mediating scientific rigor with Collingwood’s ‘imaginary’ Bateson brought about his own conception of mediated ‘thirdness’—different from C.S. Peirce—but one which brought cultural ‘mind’ more closely into association with ‘the mind of nature’. Full article

(This article belongs to the Special Issue Cybersemiotics—Integration of the informational and semiotic paradigms of cognition and communication)

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Entropy, Volume 12, Issue 12 (December 2010) – 9 articles , Pages 2359-2503

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