Entropy

183 KiB

Open AccessArticle

Entropy Production during Asymptotically Safe Inflation

by Alfio Bonanno and Martin Reuter

Entropy 2011, 13(1), 274-292; https://doi.org/10.3390/e13010274 - 24 Jan 2011

Cited by 20 | Viewed by 7015

The Asymptotic Safety scenario predicts that the deep ultraviolet of Quantum Einstein Gravity is governed by a nontrivial renormalization group fixed point. Analyzing its implications for cosmology using renormalization group improved Einstein equations, we find that it can give rise to a phase [...] Read more.

The Asymptotic Safety scenario predicts that the deep ultraviolet of Quantum Einstein Gravity is governed by a nontrivial renormalization group fixed point. Analyzing its implications for cosmology using renormalization group improved Einstein equations, we find that it can give rise to a phase of inflationary expansion in the early Universe. Inflation is a pure quantum effect here and requires no inflaton field. It is driven by the cosmological constant and ends automatically when the renormalization group evolution has reduced the vacuum energy to the level of the matter energy density. The quantum gravity effects also provide a natural mechanism for the generation of entropy. It could easily account for the entire entropy of the present Universe in the massless sector. Full article

(This article belongs to the Special Issue Entropy in Quantum Gravity)

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261 KiB

Open AccessArticle

Information Theory in Scientific Visualization

by Chaoli Wang and Han-Wei Shen

Entropy 2011, 13(1), 254-273; https://doi.org/10.3390/e13010254 - 21 Jan 2011

Cited by 93 | Viewed by 12084

Abstract

In recent years, there is an emerging direction that leverages information theory to solve many challenging problems in scientific data analysis and visualization. In this article, we review the key concepts in information theory, discuss how the principles of information theory can be [...] Read more.

In recent years, there is an emerging direction that leverages information theory to solve many challenging problems in scientific data analysis and visualization. In this article, we review the key concepts in information theory, discuss how the principles of information theory can be useful for visualization, and provide specific examples to draw connections between data communication and data visualization in terms of how information can be measured quantitatively. As the amount of digital data available to us increases at an astounding speed, the goal of this article is to introduce the interested readers to this new direction of data analysis research, and to inspire them to identify new applications and seek solutions using information theory. Full article

(This article belongs to the Special Issue Advances in Information Theory)

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128 KiB

Open AccessArticle

Wavelet-Based Multi-Scale Entropy Analysis of Complex Rainfall Time Series

by Chien-Ming Chou

Entropy 2011, 13(1), 241-253; https://doi.org/10.3390/e13010241 - 20 Jan 2011

Cited by 46 | Viewed by 7846

Abstract

This paper presents a novel framework to determine the number of resolution levels in the application of a wavelet transformation to a rainfall time series. The rainfall time series are decomposed using the à trous wavelet transform. Then, multi-scale entropy (MSE) analysis that [...] Read more.

This paper presents a novel framework to determine the number of resolution levels in the application of a wavelet transformation to a rainfall time series. The rainfall time series are decomposed using the à trous wavelet transform. Then, multi-scale entropy (MSE) analysis that helps to elucidate some hidden characteristics of the original rainfall time series is applied to the decomposed rainfall time series. The analysis shows that the Mann-Kendall (MK) rank correlation test of MSE curves of residuals at various resolution levels could determine the number of resolution levels in the wavelet decomposition. The complexity of rainfall time series at four stations on a multi-scale is compared. The results reveal that the suggested number of resolution levels can be obtained using MSE analysis and MK test. The complexity of rainfall time series at various locations can also be analyzed to provide a reference for water resource planning and application. Full article

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500 KiB

Open AccessReview

Understanding Atmospheric Behaviour in Terms of Entropy: A Review of Applications of the Second Law of Thermodynamics to Meteorology

by Ying Liu, Chongjian Liu and Donghai Wang

Entropy 2011, 13(1), 211-240; https://doi.org/10.3390/e13010211 - 19 Jan 2011

Cited by 39 | Viewed by 16436

Abstract

The concept of entropy and its relevant principles, mainly the principle of maximum entropy production (MEP), the effect of negative entropy flow (NEF) on the organization of atmospheric systems and the principle of the Second Law of thermodynamics, as well as their applications [...] Read more.

The concept of entropy and its relevant principles, mainly the principle of maximum entropy production (MEP), the effect of negative entropy flow (NEF) on the organization of atmospheric systems and the principle of the Second Law of thermodynamics, as well as their applications to atmospheric sciences, are reviewed. Some formulations of sub-grid processes such as diffusion parameterization schemes in computational geophysical fluid dynamics that can be improved based on full-irreversibility are also discussed, although they have not yet been systematically subjected to scrutiny from the perspective of the entropy budgets. A comparative investigation shows that the principle of MEP applies to the entropy production of macroscopic fluxes and determines the most probable state, that is, a system may choose a development meta-stable trajectory with a smaller production since entropy production behavior involves many specific dynamical and thermodynamic processes in the atmosphere and the extremal principles only provide a general insight into the overall configuration of the atmosphere. In contrast to the principle of MEP, the analysis of NEF is able to provide a new insight into the mechanism responsible for the evolution of a weather system as well as a new approach to predicting its track and intensity trend. Full article

(This article belongs to the Section Entropy Reviews)

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229 KiB

Open AccessArticle

Wavelet-Based Analysis on the Complexity of Hydrologic Series Data under Multi-Temporal Scales

by Yan-Fang Sang, Dong Wang, Ji-Chun Wu, Qing-Ping Zhu and Ling Wang

Entropy 2011, 13(1), 195-210; https://doi.org/10.3390/e13010195 - 17 Jan 2011

Cited by 33 | Viewed by 9496

Abstract

In this paper, the influence of four key issues on wavelet-based analysis of hydrologic series’ complexity under multi-temporal scales, including the choice of mother wavelet, noise, estimation of probability density function and trend of series data, was first studied. Then, the complexities of [...] Read more.

In this paper, the influence of four key issues on wavelet-based analysis of hydrologic series’ complexity under multi-temporal scales, including the choice of mother wavelet, noise, estimation of probability density function and trend of series data, was first studied. Then, the complexities of several representative hydrologic series data were quantified and described, based on which the performances of four wavelet-based entropy measures used commonly, namely continuous wavelet entropy (CWE), continuous wavelet relative entropy (CWRE), discrete wavelet entropy (DWE) and discrete wavelet relative entropy (DWRE) respectively, were compared and discussed. Finally, according to the analytic results of various examples, some understanding and conclusions about the calculation of wavelet-based entropy values gained in this study have been summarized, and the corresponding suggestions have also been proposed, based on which the analytic results of complexity of hydrologic series data can be improved. Full article

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113 KiB

Open AccessReview

Extreme Fisher Information, Non-Equilibrium Thermodynamics and Reciprocity Relations

by Silvana Flego, Felipe Olivares, Angelo Plastino and Montserrat Casas

Entropy 2011, 13(1), 184-194; https://doi.org/10.3390/e13010184 - 14 Jan 2011

Cited by 8 | Viewed by 7364

Abstract

In employing MaxEnt, a crucial role is assigned to the reciprocity relations that relate the quantifier to be extremized (Shannon’s entropy S), the Lagrange multipliers that arise during the variational process, and the expectation values that constitute the a priori input information. We [...] Read more.

In employing MaxEnt, a crucial role is assigned to the reciprocity relations that relate the quantifier to be extremized (Shannon’s entropy S), the Lagrange multipliers that arise during the variational process, and the expectation values that constitute the a priori input information. We review here just how these ingredients relate to each other when the information quantifier S is replaced by Fisher’s information measure I. The connection of these proceedings with thermodynamics constitute our physical background. Full article

(This article belongs to the Special Issue Advances in Information Theory)

210 KiB

Open AccessArticle

Finite-Time Thermoeconomic Optimization of a Solar-Driven Heat Engine Model

by Marco A. Barranco-Jimenez, Norma Sanchez-Salas and Fernando Angulo-Brown

Entropy 2011, 13(1), 171-183; https://doi.org/10.3390/e13010171 - 14 Jan 2011

Cited by 24 | Viewed by 7481

Abstract

In the present paper, the thermoeconomic optimization of an irreversible solar-driven heat engine model has been carried out by using finite-time/finite-size thermodynamic theory. In our study we take into account losses due to heat transfer across finite time temperature differences, heat leakage between [...] Read more.

In the present paper, the thermoeconomic optimization of an irreversible solar-driven heat engine model has been carried out by using finite-time/finite-size thermodynamic theory. In our study we take into account losses due to heat transfer across finite time temperature differences, heat leakage between thermal reservoirs and internal irreversibilities in terms of a parameter which comes from the Clausius inequality. In the considered heat engine model, the heat transfer from the hot reservoir to the working fluid is assumed to be Dulong-Petit type and the heat transfer to the cold reservoir is assumed of the Newtonian type. In this work, the optimum performance and two design parameters have been investigated under two objective functions: the power output per unit total cost and the ecological function per unit total cost. The effects of the technical and economical parameters on the thermoeconomic performance have been also discussed under the aforementioned two criteria of performance. Full article

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847 KiB

Open AccessArticle

Generalized Alpha-Beta Divergences and Their Application to Robust Nonnegative Matrix Factorization

by Andrzej Cichocki, Sergio Cruces and Shun-ichi Amari

Entropy 2011, 13(1), 134-170; https://doi.org/10.3390/e13010134 - 14 Jan 2011

Cited by 169 | Viewed by 12238

Abstract

We propose a class of multiplicative algorithms for Nonnegative Matrix Factorization (NMF) which are robust with respect to noise and outliers. To achieve this, we formulate a new family generalized divergences referred to as the Alpha-Beta-divergences (AB-divergences), which are parameterized by the two [...] Read more.

We propose a class of multiplicative algorithms for Nonnegative Matrix Factorization (NMF) which are robust with respect to noise and outliers. To achieve this, we formulate a new family generalized divergences referred to as the Alpha-Beta-divergences (AB-divergences), which are parameterized by the two tuning parameters, alpha and beta, and smoothly connect the fundamental Alpha-, Beta- and Gamma-divergences. By adjusting these tuning parameters, we show that a wide range of standard and new divergences can be obtained. The corresponding learning algorithms for NMF are shown to integrate and generalize many existing ones, including the Lee-Seung, ISRA (Image Space Reconstruction Algorithm), EMML (Expectation Maximization Maximum Likelihood), Alpha-NMF, and Beta-NMF. Owing to more degrees of freedom in tuning the parameters, the proposed family of AB-multiplicative NMF algorithms is shown to improve robustness with respect to noise and outliers. The analysis illuminates the links of between AB-divergence and other divergences, especially Gamma- and Itakura-Saito divergences. Full article

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172 KiB

Open AccessArticle

Mean-Variance-Skewness-Entropy Measures: A Multi-Objective Approach for Portfolio Selection

by Ilhan Usta and Yeliz Mert Kantar

Entropy 2011, 13(1), 117-133; https://doi.org/10.3390/e13010117 - 12 Jan 2011

Cited by 61 | Viewed by 9115

Abstract

In this study, we present a multi-objective approach based on a mean-variance-skewness-entropy portfolio selection model (MVSEM). In this approach, an entropy measure is added to the mean-variance-skewness model (MVSM) to generate a well‑diversified portfolio. Through a variety of empirical data sets, we evaluate [...] Read more.

In this study, we present a multi-objective approach based on a mean-variance-skewness-entropy portfolio selection model (MVSEM). In this approach, an entropy measure is added to the mean-variance-skewness model (MVSM) to generate a well‑diversified portfolio. Through a variety of empirical data sets, we evaluate the performance of the MVSEM in terms of several portfolio performance measures. The obtained results show that the MVSEM performs well out-of sample relative to traditional portfolio selection models. Full article

365 KiB

Open AccessReview

Entropy Production: Its Role in Non-Equilibrium Thermodynamics

by Rosa Maria Velasco, Leopoldo Scherer García-Colín and Francisco Javier Uribe

Entropy 2011, 13(1), 82-116; https://doi.org/10.3390/e13010082 - 07 Jan 2011

Cited by 37 | Viewed by 11625

Abstract

It is unquestionable that the concept of entropy has played an essential role both in the physical and biological sciences. However, the entropy production, crucial to the second law, has also other features not clearly conceived. We all know that the main difficulty [...] Read more.

It is unquestionable that the concept of entropy has played an essential role both in the physical and biological sciences. However, the entropy production, crucial to the second law, has also other features not clearly conceived. We all know that the main difficulty is concerned with its quantification in non-equilibrium processes and consequently its value for some specific cases is limited. In this work we will review the ideas behind the entropy production concept and we will give some insights about its relevance. Full article

258 KiB

Open AccessArticle

A Pattern Construction Scheme for Neural Network-Based Cognitive Communication

by Berk Ustundag and Ozgur Orcay

Entropy 2011, 13(1), 64-81; https://doi.org/10.3390/e13010064 - 07 Jan 2011

Cited by 7 | Viewed by 7119

Abstract

Inefficient utilization of the frequency spectrum due to conventional regulatory limitations and physical performance limiting factors, mainly the Signal to Noise Ratio (SNR), are prominent restrictions in digital wireless communication. Pattern Based Communication System (PBCS) is an adaptive and perceptual communication method based [...] Read more.

Inefficient utilization of the frequency spectrum due to conventional regulatory limitations and physical performance limiting factors, mainly the Signal to Noise Ratio (SNR), are prominent restrictions in digital wireless communication. Pattern Based Communication System (PBCS) is an adaptive and perceptual communication method based on a Cognitive Radio (CR) approach. It intends an SNR oriented cognition mechanism in the physical layer for improvement of Link Spectral Efficiency (LSE). The key to this system is construction of optimal communication signals, which consist of encoded data in different pattern forms (waveforms) depending on spectral availabilities. The signals distorted in the communication medium are recovered according to the pre-trained pattern glossary by the perceptual receiver. In this study, we have shown that it is possible to improve the bandwidth efficiency when largely uncorrelated signal patterns are chosen in order to form a glossary that represents symbols for different length data groups and the information can be recovered by the Artificial Neural Network (ANN) in the receiver site. Full article

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76 KiB

Open AccessCommunication

A Unique Perspective on Data Coding and Decoding

by Wen-Yan Wang

Entropy 2011, 13(1), 53-63; https://doi.org/10.3390/e13010053 - 27 Dec 2010

Cited by 2 | Viewed by 5908

Abstract

The concept of a loss-less data compression coding method is proposed, and a detailed description of each of its steps follows. Using the Calgary Corpus and Wikipedia data as the experimental samples and compared with existing algorithms, like PAQ or PPMstr, the new [...] Read more.

The concept of a loss-less data compression coding method is proposed, and a detailed description of each of its steps follows. Using the Calgary Corpus and Wikipedia data as the experimental samples and compared with existing algorithms, like PAQ or PPMstr, the new coding method could not only compress the source data, but also further re-compress the data produced by the other compression algorithms. The final files are smaller, and by comparison with the original compression ratio, at least 1% redundancy could be eliminated. The new method is simple and easy to realize. Its theoretical foundation is currently under study. The corresponding Matlab source code is provided in the Appendix. Full article

158 KiB

Open AccessArticle

An Information Approach to the Dynamics in Farm Income: Implications for Farmland Markets

by Matthew J. Salois and Charles B. Moss

Entropy 2011, 13(1), 38-52; https://doi.org/10.3390/e13010038 - 24 Dec 2010

Cited by 8 | Viewed by 7416

Abstract

The valuation of farmland is a perennial issue for agricultural policy, given its importance in the farm investment portfolio. Despite the significance of farmland values to farmer wealth, prediction remains a difficult task. This study develops a dynamic information measure to examine the [...] Read more.

The valuation of farmland is a perennial issue for agricultural policy, given its importance in the farm investment portfolio. Despite the significance of farmland values to farmer wealth, prediction remains a difficult task. This study develops a dynamic information measure to examine the informational content of farmland values and farm income in explaining the distribution of farmland values over time. Full article

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

302 KiB

Open AccessArticle

Complexity through Recombination: From Chemistry to Biology

by Niles Lehman, Carolina Díaz Arenas, Wesley A. White and Francis J. Schmidt

Entropy 2011, 13(1), 17-37; https://doi.org/10.3390/e13010017 - 24 Dec 2010

Cited by 9 | Viewed by 9014

Abstract

Recombination is a common event in nature, with examples in physics, chemistry, and biology. This process is characterized by the spontaneous reorganization of structural units to form new entities. Upon reorganization, the complexity of the overall system can change. In particular the components [...] Read more.

Recombination is a common event in nature, with examples in physics, chemistry, and biology. This process is characterized by the spontaneous reorganization of structural units to form new entities. Upon reorganization, the complexity of the overall system can change. In particular the components of the system can now experience a new response to externally applied selection criteria, such that the evolutionary trajectory of the system is altered. In this work we explore the link between chemical and biological forms of recombination. We estimate how the net system complexity changes, through analysis of RNA-RNA recombination and by mathematical modeling. Our results underscore the importance of recombination in the origins of life on the Earth and its subsequent evolutionary divergence. Full article

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

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100 KiB

Open AccessArticle

Corrections to Bekenstein-Hawking Entropy— Quantum or not-so Quantum?

by S. Shankaranarayanan

Entropy 2011, 13(1), 11-16; https://doi.org/10.3390/e13010011 - 24 Dec 2010

Cited by 3 | Viewed by 8058

Abstract

Hawking radiation and Bekenstein-Hawking entropy are the two robust predictions of a yet unknown quantum theory of gravity. Any theory which fails to reproduce these predictions is certainly incorrect. While several approaches lead to Bekenstein-Hawking entropy, they all lead to different sub-leading corrections. [...] Read more.

Hawking radiation and Bekenstein-Hawking entropy are the two robust predictions of a yet unknown quantum theory of gravity. Any theory which fails to reproduce these predictions is certainly incorrect. While several approaches lead to Bekenstein-Hawking entropy, they all lead to different sub-leading corrections. In this article, we ask a question that is relevant for any approach: Using simple techniques, can we know whether an approach contains quantum or semi-classical degrees of freedom? Using naive dimensional analysis, we show that the semi-classical black-hole entropy has the same dimensional dependence as the gravity action. Among others, this provides a plausible explanation for the connection between Einstein’s equations and thermodynamic equation of state, and that the quantum corrections should have a different scaling behavior. Full article

(This article belongs to the Special Issue Entropy in Quantum Gravity)

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242 KiB

Open AccessArticle

Information Storage in Liquids with Ordered Molecular Assemblies

by Meir Shinitzky

Entropy 2011, 13(1), 1-10; https://doi.org/10.3390/e13010001 - 23 Dec 2010

Viewed by 6181

Abstract

In some unique cases, liquids can divert from pure isotropy due to the formation of ordered molecular assemblies with acquired “negative entropy” and information storage. The energy stored in such ordered domains can be combined with an independent quantitative parameter related to the [...] Read more.

In some unique cases, liquids can divert from pure isotropy due to the formation of ordered molecular assemblies with acquired “negative entropy” and information storage. The energy stored in such ordered domains can be combined with an independent quantitative parameter related to the degree of order, which can then translate the dormant information to the quantitative energetic term “information capacity”. Information storage in liquids can be thus expressed in absolute energy units. Three liquid systems are analyzed in some detail. The first is a solution of a chiral substance, e.g., amino acid in water, where the degree of optical rotation provides the measure for order while the heat liberated upon racemization is the energy corresponding to the negative entropy. The second is a neat chiral fluid, e.g., 2-butanol, complying with the same parameters as those of chiral solutions. The third is electronically excited fluorescent solute, where the shift in the emission spectrum corresponds to the energy acquired by the transiently oriented solvent envelopes. Other, yet unexplored, possibilities are also suggested. Full article

(This article belongs to the Special Issue Advances in Information Theory)

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Entropy, Volume 13, Issue 1 (January 2011) – 16 articles , Pages 1-292

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