Entropy

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Open AccessEditorial

Acknowledgement to Reviewers of Entropy in 2015

by Entropy Editorial Office

Entropy 2016, 18(1), 37; https://doi.org/10.3390/e18010037 - 21 Jan 2016

Viewed by 5700

The editors of Entropy would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2015. [...] Full article

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Open AccessArticle

The Entropy of Laughter: Discriminative Power of Laughter’s Entropy in the Diagnosis of Depression

by Jorge Navarro, Raquel Del Moral, Pedro Cuesta-Alvaro, Rafael Lahoz-Beltra and Pedro C. Marijuán

Entropy 2016, 18(1), 36; https://doi.org/10.3390/e18010036 - 21 Jan 2016

Cited by 4 | Viewed by 9301

Abstract

Laughter is increasingly present in biomedical literature, both in analytical neurological aspects and in applied therapeutic fields. The present paper, bridging between the analytical and the applied, explores the potential of a relevant variable of laughter’s acoustic signature—entropy—in the detection of a widespread [...] Read more.

Laughter is increasingly present in biomedical literature, both in analytical neurological aspects and in applied therapeutic fields. The present paper, bridging between the analytical and the applied, explores the potential of a relevant variable of laughter’s acoustic signature—entropy—in the detection of a widespread mental disorder, depression, as well as in gauging the severity of its diagnostic. In laughter, the Shannon–Wiener entropy of the distribution of sound frequencies, which is one of the key features distinguishing its acoustic signal from the utterances of spoken language, has not been a specific focus of research yet, although the studies of human language and of animal communication have pointed out that entropy is a very important factor regarding the vocal/acoustic expression of emotions. As the experimental survey of laughter in depression herein undertaken shows, it was possible to discriminate between patients and controls with an 82.1% accuracy just by using laughter’s entropy and by applying the decision tree procedure. These experimental results, discussed in the light of the current research on laughter, point to the relevance of entropy in the spontaneous bona fide extroversion of mental states toward other individuals, as the signal of laughter seems to imply. This is in line with recent theoretical approaches that rely on the optimization of a neuro-informational free energy (and associated entropy) as the main “stuff” of brain processing. Full article

(This article belongs to the Special Issue Recent Advances in Information Theory Application to Physiological Signals)

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Open AccessArticle

Average Contrastive Divergence for Training Restricted Boltzmann Machines

by Xuesi Ma and Xiaojie Wang

Entropy 2016, 18(1), 35; https://doi.org/10.3390/e18010035 - 21 Jan 2016

Cited by 15 | Viewed by 4946

Abstract

This paper studies contrastive divergence (CD) learning algorithm and proposes a new algorithm for training restricted Boltzmann machines (RBMs). We derive that CD is a biased estimator of the log-likelihood gradient method and make an analysis of the bias. Meanwhile, we propose a [...] Read more.

This paper studies contrastive divergence (CD) learning algorithm and proposes a new algorithm for training restricted Boltzmann machines (RBMs). We derive that CD is a biased estimator of the log-likelihood gradient method and make an analysis of the bias. Meanwhile, we propose a new learning algorithm called average contrastive divergence (ACD) for training RBMs. It is an improved CD algorithm, and it is different from the traditional CD algorithm. Finally, we obtain some experimental results. The results show that the new algorithm is a better approximation of the log-likelihood gradient method and outperforms the traditional CD algorithm. Full article

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Open AccessArticle

Schroedinger vs. Navier–Stokes

by P. Fernández de Córdoba, J. M. Isidro and J. Vázquez Molina

Entropy 2016, 18(1), 34; https://doi.org/10.3390/e18010034 - 19 Jan 2016

Cited by 6 | Viewed by 6083

Abstract

Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier–Stokes equation for viscous fluid flow. [...] Read more.

Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier–Stokes equation for viscous fluid flow. As a physical model for the fluid itself we propose the quantum probability fluid. It turns out that the (state-dependent) viscosity of this fluid is proportional to Planck’s constant, while the volume density of entropy is proportional to Boltzmann’s constant. Stationary states have zero viscosity and a vanishing time rate of entropy density. On the other hand, the nonzero viscosity of nonstationary states provides an information-loss mechanism whereby a deterministic theory (a classical fluid governed by the Navier–Stokes equation) gives rise to an emergent theory (a quantum particle governed by the Schroedinger equation). Full article

(This article belongs to the Special Issue Quantum Thermodynamics)

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Open AccessArticle

Measure of Uncertainty in Process Models Using Stochastic Petri Nets and Shannon Entropy

by Martin Ibl and Jan Čapek

Entropy 2016, 18(1), 33; https://doi.org/10.3390/e18010033 - 19 Jan 2016

Cited by 13 | Viewed by 5427

Abstract

When modelling and analysing business processes, the main emphasis is usually put on model validity and accuracy, i.e., the model meets the formal specification and also models the relevant system. In recent years, a series of metrics has begun to develop, which [...] Read more.

When modelling and analysing business processes, the main emphasis is usually put on model validity and accuracy, i.e., the model meets the formal specification and also models the relevant system. In recent years, a series of metrics has begun to develop, which allows the quantification of the specific properties of process models. These characteristics are, for instance, complexity, comprehensibility, cohesion, and uncertainty. This work is focused on defining a method that allows us to measure the uncertainty of a process model, which was modelled by using stochastic Petri nets (SPN). The principle of this method consists of mapping of all reachable marking of SPN into the continuous-time Markov chain and then calculating its stationary probabilities. The uncertainty is then measured as the entropy of the Markov chain (it is possible to calculate the uncertainty of the specific subset of places as well as of whole net). Alternatively, the uncertainty index is quantified as a percentage of the calculated entropy against maximum entropy (the resulting value is normalized to the interval <0,1>). The calculated entropy can also be used as a measure of the model complexity. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

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Open AccessArticle

Predicting Traffic Flow in Local Area Networks by the Largest Lyapunov Exponent

by Yan Liu and Jiazhong Zhang

Entropy 2016, 18(1), 32; https://doi.org/10.3390/e18010032 - 19 Jan 2016

Cited by 13 | Viewed by 5428

Abstract

The dynamics of network traffic are complex and nonlinear, and chaotic behaviors and their prediction, which play an important role in local area networks (LANs), are studied in detail, using the largest Lyapunov exponent. With the introduction of phase space reconstruction based on [...] Read more.

The dynamics of network traffic are complex and nonlinear, and chaotic behaviors and their prediction, which play an important role in local area networks (LANs), are studied in detail, using the largest Lyapunov exponent. With the introduction of phase space reconstruction based on the time sequence, the high-dimensional traffic is projected onto the low dimension reconstructed phase space, and a reduced dynamic system is obtained from the dynamic system viewpoint. Then, a numerical method for computing the largest Lyapunov exponent of the low-dimensional dynamic system is presented. Further, the longest predictable time, which is related to chaotic behaviors in the system, is studied using the largest Lyapunov exponent, and the Wolf method is used to predict the evolution of the traffic in a local area network by both Dot and Interval predictions, and a reliable result is obtained by the presented method. As the conclusion, the results show that the largest Lyapunov exponent can be used to describe the sensitivity of the trajectory in the reconstructed phase space to the initial values. Moreover, Dot Prediction can effectively predict the flow burst. The numerical simulation also shows that the presented method is feasible and efficient for predicting the complex dynamic behaviors in LAN traffic, especially for congestion and attack in networks, which are the main two complex phenomena behaving as chaos in networks. Full article

(This article belongs to the Special Issue Complex and Fractional Dynamics)

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Open AccessArticle

Perturbation of Fractional Multi-Agent Systems in Cloud Entropy Computing

by Rabha W. Ibrahim, Hamid A. Jalab and Abdullah Gani

Entropy 2016, 18(1), 31; https://doi.org/10.3390/e18010031 - 19 Jan 2016

Cited by 11 | Viewed by 4391

Abstract

A perturbed multi-agent system is a scheme self-possessed of multiple networking agents within a location. This scheme can be used to discuss problems that are impossible or difficult for a specific agent to solve. Intelligence cloud entropy management systems involve functions, methods, procedural [...] Read more.

A perturbed multi-agent system is a scheme self-possessed of multiple networking agents within a location. This scheme can be used to discuss problems that are impossible or difficult for a specific agent to solve. Intelligence cloud entropy management systems involve functions, methods, procedural approaches, and algorithms. In this study, we introduce a new perturbed algorithm based on the fractional Poisson process. The discrete dynamics are suggested by using fractional entropy and fractional type Tsallis entropy. Moreover, we study the algorithm stability. Full article

(This article belongs to the Special Issue Computational Complexity)

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Open AccessArticle

Distributed Consensus of Nonlinear Multi-Agent Systems on State-Controlled Switching Topologies

by Kairui Chen, Junwei Wang and Yun Zhang

Entropy 2016, 18(1), 29; https://doi.org/10.3390/e18010029 - 18 Jan 2016

Cited by 6 | Viewed by 4693

Abstract

This paper considers the consensus problem of nonlinear multi-agent systems under switching directed topologies. Specifically, the dynamics of each agent incorporates an intrinsic nonlinear term and the interaction topology may not contain a spanning tree at any time. By designing a state-controlled switching [...] Read more.

This paper considers the consensus problem of nonlinear multi-agent systems under switching directed topologies. Specifically, the dynamics of each agent incorporates an intrinsic nonlinear term and the interaction topology may not contain a spanning tree at any time. By designing a state-controlled switching law, we show that the multi-agent system with the neighbor-based protocol can achieve consensus if the switching topologies jointly contain a spanning tree. Moreover, an easily manageable algebraic criterion is deduced to unravel the underlying mechanisms in reaching consensus. Finally, a numerical example is exploited to illustrate the effectiveness of the developed theoretical results. Full article

(This article belongs to the Section Complexity)

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Open AccessArticle

Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems

by Dagmar Markechová and Beloslav Riečan

Entropy 2016, 18(1), 19; https://doi.org/10.3390/e18010019 - 18 Jan 2016

Cited by 25 | Viewed by 5150

Abstract

In the paper we define three kinds of entropy of a fuzzy dynamical system using different entropies of fuzzy partitions. It is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamical systems. The [...] Read more.

In the paper we define three kinds of entropy of a fuzzy dynamical system using different entropies of fuzzy partitions. It is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamical systems. The relationships between these entropies are studied and connections with the classical case are mentioned as well. Finally, an analogy of the Kolmogorov–Sinai Theorem on generators is proved for fuzzy dynamical systems. Full article

(This article belongs to the Section Complexity)

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Open AccessArticle

Using Multidimensional ADTPE and SVM for Optical Modulation Real-Time Recognition

by Junyu Wei, Zhiping Huang, Shaojing Su and Zhen Zuo

Entropy 2016, 18(1), 30; https://doi.org/10.3390/e18010030 - 16 Jan 2016

Cited by 6 | Viewed by 5604

Abstract

Based on the feature extraction of multidimensional asynchronous delay-tap plot entropy (ADTPE) and multiclass classification of support vector machine (SVM), we propose a method for recognition of multiple optical modulation formats and various data rates. We firstly present the algorithm of multidimensional ADTPE, [...] Read more.

Based on the feature extraction of multidimensional asynchronous delay-tap plot entropy (ADTPE) and multiclass classification of support vector machine (SVM), we propose a method for recognition of multiple optical modulation formats and various data rates. We firstly present the algorithm of multidimensional ADTPE, which is extracted from asynchronous delay sampling pairs of modulated optical signal. Then, a multiclass SVM is utilized for fast and accurate classification of several widely-used optical modulation formats. In addition, a simple real-time recognition scheme is designed to reduce the computation time. Compared to the existing method based on asynchronous delay-tap plot (ADTP), the theoretical analysis and simulation results show that our recognition method can effectively enhance the tolerance of transmission impairments, obtaining relatively high accuracy. Finally, it is further demonstrated that the proposed method can be integrated in an optical transport network (OTN) with flexible expansion. Through simply adding the corresponding sub-SVM module in the digital signal processer (DSP), arbitrary new modulation formats can be recognized with high recognition accuracy in a short response time. Full article

(This article belongs to the Special Issue Machine Learning and Entropy: Discover Unknown Unknowns in Complex Data Sets)

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Open AccessEditorial

Entropy Generation Results of Convenience But without Purposeful Analysis and Due Comprehension—Guidelines for Authors

by Milivoje M. Kostic

Entropy 2016, 18(1), 28; https://doi.org/10.3390/e18010028 - 15 Jan 2016

Cited by 2 | Viewed by 5260

Abstract

There is a growing trend in recently-submitted manuscripts and publications to present calculated results of entropy generation, also known as entropy production, as field quantities in a system or device control volume, based on prior calculation of velocity and temperature fields, frequently using [...] Read more.

There is a growing trend in recently-submitted manuscripts and publications to present calculated results of entropy generation, also known as entropy production, as field quantities in a system or device control volume, based on prior calculation of velocity and temperature fields, frequently using CFD numerical methods. [...] Full article

(This article belongs to the Special Issue Exploring the Second Law of Thermodynamics)

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Open AccessArticle

Interacting Brownian Swarms: Some Analytical Results

by Guillaume Sartoretti and Max-Olivier Hongler

Entropy 2016, 18(1), 27; https://doi.org/10.3390/e18010027 - 14 Jan 2016

Cited by 4 | Viewed by 4327

Abstract

We consider the dynamics of swarms of scalar Brownian agents subject to local imitation mechanisms implemented using mutual rank-based interactions. For appropriate values of the underlying control parameters, the swarm propagates tightly and the distances separating successive agents are iid exponential random variables. [...] Read more.

We consider the dynamics of swarms of scalar Brownian agents subject to local imitation mechanisms implemented using mutual rank-based interactions. For appropriate values of the underlying control parameters, the swarm propagates tightly and the distances separating successive agents are iid exponential random variables. Implicitly, the implementation of rank-based mutual interactions, requires that agents have infinite interaction ranges. Using the probabilistic size of the swarm’s support, we analytically estimate the critical interaction range below that flocked swarms cannot survive. In the second part of the paper, we consider the interactions between two flocked swarms of Brownian agents with finite interaction ranges. Both swarms travel with different barycentric velocities, and agents from both swarms indifferently interact with each other. For appropriate initial configurations, both swarms eventually collide (i.e., all agents interact). Depending on the values of the control parameters, one of the following patterns emerges after collision: (i) Both swarms remain essentially flocked, or (ii) the swarms become ultimately quasi-free and recover their nominal barycentric speeds. We derive a set of analytical flocking conditions based on the generalized rank-based Brownian motion. An extensive set of numerical simulations corroborates our analytical findings. Full article

(This article belongs to the Special Issue Recent Advances in Non-Equilibrium Statistical Mechanics and Its Application)

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Open AccessArticle

Information and the Quantum World

by Dennis Dieks

Entropy 2016, 18(1), 26; https://doi.org/10.3390/e18010026 - 13 Jan 2016

Cited by 5 | Viewed by 4595

Abstract

The concept of information is not different in quantum theory from its counterpart in classical physics: a sui generis quantum information concept is not needed. However, the quantum world is radically different from its classical counterpart. This difference in structure of the material [...] Read more.

The concept of information is not different in quantum theory from its counterpart in classical physics: a sui generis quantum information concept is not needed. However, the quantum world is radically different from its classical counterpart. This difference in structure of the material world has important consequences for the amounts of information that can be stored in physical systems and for the possibilities of information transfer. In many cases, overlap between quantum states (non-orthogonality of states) blurs distinctions and impedes efficient information transfer. However, the other typical quantum feature, entanglement, makes new and seemingly mysterious ways of transporting information possible. In this article, we suggest an interpretational scheme of quantum mechanics in terms of perspectival physical properties that may provide an intelligible account of these novel quantum possibilities, while staying close to the mathematical formalism of quantum mechanics. Full article

(This article belongs to the Special Issue Information: Meanings and Interpretations)

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Open AccessArticle

Hot Spots and Persistence of Nitrate in Aquifers Across Scales

by Dipankar Dwivedi and Binayak P. Mohanty

Entropy 2016, 18(1), 25; https://doi.org/10.3390/e18010025 - 13 Jan 2016

Cited by 20 | Viewed by 5362

Abstract

Nitrate-N (NO₃^-- N) is one of the most pervasive contaminants in groundwater. Nitrate in groundwater exhibits long-term behavior due to complex interactions at multiple scales among various geophysical factors, such as sources of nitrate-N, characteristics of the vadose zone and [...] Read more.

Nitrate-N (NO₃^-- N) is one of the most pervasive contaminants in groundwater. Nitrate in groundwater exhibits long-term behavior due to complex interactions at multiple scales among various geophysical factors, such as sources of nitrate-N, characteristics of the vadose zone and aquifer attributes. To minimize contamination of nitrate-N in groundwater, it is important to estimate hot spots (>10 mg/L of NO₃^-- N), trends and persistence of nitrate-N in groundwater. To analyze the trends and persistence of nitrate-N in groundwater at multiple spatio-temporal scales, we developed and used an entropy-based method along with the Hurst exponent in two different hydrogeologic settings: the Trinity and Ogallala Aquifers in Texas at fine (2 km × 2 km), intermediate (10 km × 10 km) and coarse (100 km × 100 km) scales. Results show that nitrate-N exhibits long-term persistence at the intermediate and coarse scales. In the Trinity Aquifer, overall mean nitrate-N has declined with a slight increase in normalized marginal entropy (NME) over each decade from 1940 to 2008; however, the number of hot spots has increased over time. In the Ogallala Aquifer, overall mean nitrate-N has increased with slight moderation in NME since 1940; however, the number of hot spots has significantly decreased for the same period at all scales. Full article

(This article belongs to the Special Issue Applications of Information Theory in the Geosciences)

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Open AccessTechnical Note

Entropy Analysis of Solar Two-Step Thermochemical Cycles for Water and Carbon Dioxide Splitting

by Matthias Lange, Martin Roeb, Christian Sattler and Robert Pitz-Paal

Entropy 2016, 18(1), 24; https://doi.org/10.3390/e18010024 - 11 Jan 2016

Cited by 12 | Viewed by 8033

Abstract

The present study provides a thermodynamic analysis of solar thermochemical cycles for splitting of H₂O or CO₂. Such cycles, powered by concentrated solar energy, have the potential to produce fuels in a sustainable way. We extend a previous study [...] Read more.

The present study provides a thermodynamic analysis of solar thermochemical cycles for splitting of H₂O or CO₂. Such cycles, powered by concentrated solar energy, have the potential to produce fuels in a sustainable way. We extend a previous study on the thermodynamics of water splitting by also taking into account CO₂ splitting and the influence of the solar absorption efficiency. Based on this purely thermodynamic approach, efficiency trends are discussed. The comprehensive and vivid representation in T-S diagrams provides researchers in this field with the required theoretical background to improve process development. Furthermore, results about the required entropy change in the used redox materials can be used as a guideline for material developers. The results show that CO₂ splitting is advantageous at higher temperature levels, while water splitting is more feasible at lower temperature levels, as it benefits from a great entropy change during the splitting step. Full article

(This article belongs to the Special Issue Selected Papers from 13th Joint European Thermodynamics Conference)

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Open AccessArticle

Long Range Dependence Prognostics for Bearing Vibration Intensity Chaotic Time Series

by Qing Li, Steven Y. Liang, Jianguo Yang and Beizhi Li

Entropy 2016, 18(1), 23; https://doi.org/10.3390/e18010023 - 8 Jan 2016

Cited by 31 | Viewed by 6140

Abstract

According to the chaotic features and typical fractional order characteristics of the bearing vibration intensity time series, a forecasting approach based on long range dependence (LRD) is proposed. In order to reveal the internal chaotic properties, vibration intensity time series are reconstructed based [...] Read more.

According to the chaotic features and typical fractional order characteristics of the bearing vibration intensity time series, a forecasting approach based on long range dependence (LRD) is proposed. In order to reveal the internal chaotic properties, vibration intensity time series are reconstructed based on chaos theory in phase-space, the delay time is computed with C-C method and the optimal embedding dimension and saturated correlation dimension are calculated via the Grassberger–Procaccia (G-P) method, respectively, so that the chaotic characteristics of vibration intensity time series can be jointly determined by the largest Lyapunov exponent and phase plane trajectory of vibration intensity time series, meanwhile, the largest Lyapunov exponent is calculated by the Wolf method and phase plane trajectory is illustrated using Duffing-Holmes Oscillator (DHO). The Hurst exponent and long range dependence prediction method are proposed to verify the typical fractional order features and improve the prediction accuracy of bearing vibration intensity time series, respectively. Experience shows that the vibration intensity time series have chaotic properties and the LRD prediction method is better than the other prediction methods (largest Lyapunov, auto regressive moving average (ARMA) and BP neural network (BPNN) model) in prediction accuracy and prediction performance, which provides a new approach for running tendency predictions for rotating machinery and provide some guidance value to the engineering practice. Full article

(This article belongs to the Section Complexity)

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Open AccessArticle

Increment Entropy as a Measure of Complexity for Time Series

by Xiaofeng Liu, Aimin Jiang, Ning Xu and Jianru Xue

Entropy 2016, 18(1), 22; https://doi.org/10.3390/e18010022 - 8 Jan 2016

Cited by 51 | Viewed by 9624 | Correction

Abstract

Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce an increment entropy to measure the complexity of time series in which each increment is mapped onto a word of two letters, [...] Read more.

Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce an increment entropy to measure the complexity of time series in which each increment is mapped onto a word of two letters, one corresponding to the sign and the other corresponding to the magnitude. Increment entropy (IncrEn) is defined as the Shannon entropy of the words. Simulations on synthetic data and tests on epileptic electroencephalogram (EEG) signals demonstrate its ability of detecting abrupt changes, regardless of the energetic (e.g., spikes or bursts) or structural changes. The computation of IncrEn does not make any assumption on time series, and it can be applicable to arbitrary real-world data. Full article

(This article belongs to the Special Issue Complex and Fractional Dynamics)

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Open AccessArticle

Entropy Assessment on Direct Contact Condensation of Subsonic Steam Jets in a Water Tank through Numerical Investigation

by Yu Ji, Hao-Chun Zhang, Jian-Fei Tong, Xu-Wei Wang, Han Wang and Yi-Ning Zhang

Entropy 2016, 18(1), 21; https://doi.org/10.3390/e18010021 - 7 Jan 2016

Cited by 18 | Viewed by 7094

Abstract

The present article analyzes the dissipation characteristics of the direct contact condensation (DCC) phenomenon that occurs when steam is injected into a water tank at a subsonic speed using a new modeling approach for the entropy generation over the calculation domain. The developed [...] Read more.

The present article analyzes the dissipation characteristics of the direct contact condensation (DCC) phenomenon that occurs when steam is injected into a water tank at a subsonic speed using a new modeling approach for the entropy generation over the calculation domain. The developed entropy assessment model is based on the local equilibrium hypothesis of non-equilibrium thermodynamics. The fluid flow and heat transfer processes are investigated numerically. To describe the condensation and evaporation process at the vapor-liquid interface, a phase change model originated from the kinetic theory of gas is implemented with the mixture model for multiphase flow in the computational fluid dynamics (CFD) code ANSYS-FLUENT. The CFD predictions agree well with the published works, which indicates the phase change model combined with the mixture model is a promising way to simulate the DCC phenomenon. In addition, three clear stages as initial stage, developing stage and oscillatory stage are discriminated from both the thermal-hydraulic results and the entropy generation information. During different stages, different proportion of the entropy generation rate owing to heat transfer, viscous direct dissipation, turbulent dissipation and inner phase change in total entropy generation rate is estimated, which is favorable to deeper understanding the irreversibility of DCC phenomenon, designing and optimizing the equipment involved in the process. Full article

(This article belongs to the Special Issue Exploring the Second Law of Thermodynamics)

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Open AccessArticle

Trusted Noise in Continuous-Variable Quantum Key Distribution: A Threat and a Defense

by Vladyslav C. Usenko and Radim Filip

Entropy 2016, 18(1), 20; https://doi.org/10.3390/e18010020 - 5 Jan 2016

Cited by 94 | Viewed by 8657

Abstract

We address the role of the phase-insensitive trusted preparation and detection noise in the security of a continuous-variable quantum key distribution, considering the Gaussian protocols on the basis of coherent and squeezed states and studying them in the conditions of Gaussian lossy and [...] Read more.

We address the role of the phase-insensitive trusted preparation and detection noise in the security of a continuous-variable quantum key distribution, considering the Gaussian protocols on the basis of coherent and squeezed states and studying them in the conditions of Gaussian lossy and noisy channels. The influence of such a noise on the security of Gaussian quantum cryptography can be crucial, even despite the fact that a noise is trusted, due to a strongly nonlinear behavior of the quantum entropies involved in the security analysis. We recapitulate the known effect of the preparation noise in both direct and reverse-reconciliation protocols, as well as the detection noise in the reverse-reconciliation scenario. As a new result, we show the negative role of the trusted detection noise in the direct-reconciliation scheme. We also describe the role of the trusted preparation or detection noise added at the reference side of the protocols in improving the robustness of the protocols to the channel noise, confirming the positive effect for the coherent-state reverse-reconciliation protocol. Finally, we address the combined effect of trusted noise added both in the source and the detector. Full article

(This article belongs to the Special Issue Quantum Cryptography)

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Open AccessArticle

Analysis of Entropy Generation in Natural Convection of Nanofluid inside a Square Cavity Having Hot Solid Block: Tiwari and Das’ Model

by Mikhail A. Sheremet, Hakan F. Oztop, Ioan Pop and Nidal Abu-Hamdeh

Entropy 2016, 18(1), 9; https://doi.org/10.3390/e18010009 - 31 Dec 2015

Cited by 116 | Viewed by 7862

Abstract

A computational work has been performed in this study to investigate the effects of solid isothermal partition insertion in a nanofluid filled cavity that is cooled via corner isothermal cooler. Mathematical model formulated in dimensionless primitive variables has been solved by finite volume [...] Read more.

A computational work has been performed in this study to investigate the effects of solid isothermal partition insertion in a nanofluid filled cavity that is cooled via corner isothermal cooler. Mathematical model formulated in dimensionless primitive variables has been solved by finite volume method. The study is performed for different geometrical ratio of solid inserted block and corner isothermal cooler, Rayleigh number and solid volume fraction parameter of nanoparticles. It is observed that an insertion of nanoparticles leads to enhancement of heat transfer and attenuation of convective flow inside the cavity. Full article

(This article belongs to the Special Issue Entropy in Nanofluids)

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Open AccessArticle

Towards the Development of a Universal Expression for the Configurational Entropy of Mixing

by Jorge Garcés

Entropy 2016, 18(1), 5; https://doi.org/10.3390/e18010005 - 31 Dec 2015

Viewed by 4867

Abstract

This work discusses the development of analytical expressions for the configurational entropy of different states of matter using a method based on the identification of the energy-independent complexes (clustering of atoms) in the system and the calculation of their corresponding probabilities. The example [...] Read more.

This work discusses the development of analytical expressions for the configurational entropy of different states of matter using a method based on the identification of the energy-independent complexes (clustering of atoms) in the system and the calculation of their corresponding probabilities. The example of short-range order (SRO) in Nb-H interstitial solid solution is used to illustrate the choice of the atomic complexes and their structural changes with H concentration, providing an alternative methodology to describe critical properties. The calculated critical composition of the miscibility gap is x_c = 0.307, in remarkable agreement with the experimental value of x_c ~ 0.31. The same methodology is applied to deduce the equation of state (EOS) of a hard sphere system. The EOS is suitable to describe the percolation thresholds and fulfills both the low and random close packing limits. The model, based on the partition of the space into Voronoi cells, can be applied to any off-lattice system, thus introducing the possibility of computing the configurational entropy of gases, liquids and glasses with the same level of accuracy. Full article

(This article belongs to the Special Issue Selected Papers from 1st International Electronic Conference on Entropy and its Applications)

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Open AccessArticle

Constitutive Explanations as a Methodological Framework for Integrating Thermodynamics and Economics

by Carsten Herrmann-Pillath

Entropy 2016, 18(1), 18; https://doi.org/10.3390/e18010018 - 31 Dec 2015

Cited by 3 | Viewed by 4991

Abstract

The common approach to integrating thermodynamics and economics is subsuming thermodynamic aspects among the set of constraints under which economic activity takes place. The causal link between energy and growth is investigated via aggregate econometric analysis. This paper discusses methodological issues of aggregate [...] Read more.

The common approach to integrating thermodynamics and economics is subsuming thermodynamic aspects among the set of constraints under which economic activity takes place. The causal link between energy and growth is investigated via aggregate econometric analysis. This paper discusses methodological issues of aggregate analysis and proposes an alternative framework based on recent developments in philosophy of science, in particular of the life sciences. “Constitutive explanations” eschew the covering law approach to scientific explanation and concentrate on the identification of multi-level architectures of causal mechanisms that generate phenomena. This methodology has been productively employed to organize cross-disciplinary research, and I suggest that it can also provide a framework for integrating thermodynamics and economics, since this also requires the combination of several scientific disciplines. I present the example of the “rebound effect” as a kind of constitutive explanation and put it in the context of urbanization as a complex mechanism that is the defining feature of economic growth in physical terms. Full article

(This article belongs to the Special Issue Entropy and the Economy)

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Open AccessArticle

Three-Dimensional Lattice Boltzmann Simulation of Liquid Water Transport in Porous Layer of PEMFC

by Bo Han, Meng Ni and Hua Meng

Entropy 2016, 18(1), 17; https://doi.org/10.3390/e18010017 - 31 Dec 2015

Cited by 25 | Viewed by 7780

Abstract

A three-dimensional two-phase lattice Boltzmann model (LBM) is implemented and validated for qualitative study of the fundamental phenomena of liquid water transport in the porous layer of a proton exchange membrane fuel cell (PEMFC). In the present study, the three-dimensional microstructures of a [...] Read more.

A three-dimensional two-phase lattice Boltzmann model (LBM) is implemented and validated for qualitative study of the fundamental phenomena of liquid water transport in the porous layer of a proton exchange membrane fuel cell (PEMFC). In the present study, the three-dimensional microstructures of a porous layer are numerically reconstructed by a random generation method. The LBM simulations focus on the effects of the porous layer porosity and boundary liquid saturation on liquid water transport in porous materials. Numerical results confirm that liquid water transport is strongly affected by the microstructures in a porous layer, and the transport process prefers the large pores as its main pathway. The preferential transport phenomenon is more profound with a decreased porous layer porosity and/or boundary liquid saturation. In the transport process, the breakup of a liquid water stream can occur under certain conditions, leading to the formation of liquid droplets inside the porous layer. This phenomenon is related to the connecting bridge or neck resistance dictated by the surface tension, and happens more frequently with a smaller porous layer porosity. Results indicate that an optimized design of porous layer porosity and the combination of various pore sizes may improve both the liquid water removal and gaseous reactant transport in the porous layer of a PEMFC. Full article

(This article belongs to the Special Issue Non-Linear Lattice)

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272 KiB

Open AccessArticle

Stochastic Reorder Point-Lot Size (r,Q) Inventory Model under Maximum Entropy Principle

by Davide Castellano

Entropy 2016, 18(1), 16; https://doi.org/10.3390/e18010016 - 30 Dec 2015

Cited by 11 | Viewed by 5082

Abstract

This paper takes into account the continuous-review reorder point-lot size (r,Q) inventory model under stochastic demand, with the backorders-lost sales mixture. Moreover, to reflect the practical circumstance in which full information about the demand distribution lacks, we assume that [...] Read more.

This paper takes into account the continuous-review reorder point-lot size (r,Q) inventory model under stochastic demand, with the backorders-lost sales mixture. Moreover, to reflect the practical circumstance in which full information about the demand distribution lacks, we assume that only an estimate of the mean and of the variance is available. Contrarily to the typical approach in which the lead-time demand is supposed Gaussian or is obtained according to the so-called minimax procedure, we take a different perspective. That is, we adopt the maximum entropy principle to model the lead-time demand distribution. In particular, we consider the density that maximizes the entropy over all distributions with given mean and variance. With the aim of minimizing the expected total cost per time unit, we then propose an exact algorithm and a heuristic procedure. The heuristic method exploits an approximated expression of the total cost function achieved by means of an ad hoc first-order Taylor polynomial. We finally carry out numerical experiments with a twofold objective. On the one hand we examine the efficiency of the approximated solution procedure. On the other hand we investigate the performance of the maximum entropy principle in approximating the true lead-time demand distribution. Full article

(This article belongs to the Special Issue Entropy, Utility, and Logical Reasoning)

8850 KiB

Open AccessArticle

Thermal Characteristics of a Primary Surface Heat Exchanger with Corrugated Channels

by Jang-Won Seo, Chanyong Cho, Sangrae Lee and Young-Don Choi

Entropy 2016, 18(1), 15; https://doi.org/10.3390/e18010015 - 30 Dec 2015

Cited by 19 | Viewed by 7528

Abstract

This paper presents the heat transfer and pressure drop characteristics of a primary surface heat exchanger (PSHE) with corrugated surfaces. The PSHE was experimentally investigated for a Reynolds number range of 156–921 under various flow conditions on the hot and cold sides. The [...] Read more.

This paper presents the heat transfer and pressure drop characteristics of a primary surface heat exchanger (PSHE) with corrugated surfaces. The PSHE was experimentally investigated for a Reynolds number range of 156–921 under various flow conditions on the hot and cold sides. The inlet temperature of the hot side was maintained at 40 °C, while that of the cold side was maintained at 20 °C. A counterflow was used as it has a higher temperature proximity in comparison with a parallel flow. The heat transfer rate and pressure drop were measured for various Reynolds numbers on both the hot and cold sides of the PSHE, with the heat transfer coefficients for both sides computed using a modified Wilson plot method. Based on the results of the experiment, both Nusselt number and friction factor correlations were suggested for a PSHE with corrugated surfaces. Full article

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2450 KiB

Open AccessArticle

Wavelet Energy and Wavelet Coherence as EEG Biomarkers for the Diagnosis of Parkinson’s Disease-Related Dementia and Alzheimer’s Disease

by Dong-Hwa Jeong, Young-Do Kim, In-Uk Song, Yong-An Chung and Jaeseung Jeong

Entropy 2016, 18(1), 8; https://doi.org/10.3390/e18010008 - 29 Dec 2015

Cited by 52 | Viewed by 9512

Abstract

Parkinson’s disease (PD) and Alzheimer’s disease (AD) can coexist in severely affected; elderly patients. Since they have different pathological causes and lesions and consequently require different treatments; it is critical to distinguish PD-related dementia (PD-D) from AD. Conventional electroencephalograph (EEG) analysis has produced [...] Read more.

Parkinson’s disease (PD) and Alzheimer’s disease (AD) can coexist in severely affected; elderly patients. Since they have different pathological causes and lesions and consequently require different treatments; it is critical to distinguish PD-related dementia (PD-D) from AD. Conventional electroencephalograph (EEG) analysis has produced poor results. This study investigated the possibility of using relative wavelet energy (RWE) and wavelet coherence (WC) analysis to distinguish between PD-D patients; AD patients and healthy elderly subjects. In EEG signals; we found that low-frequency wavelet energy increased and high-frequency wavelet energy decreased in PD-D patients and AD patients relative to healthy subjects. This result suggests that cognitive decline in both diseases is potentially related to slow EEG activity; which is consistent with previous studies. More importantly; WC values were lower in AD patients and higher in PD-D patients compared with healthy subjects. In particular; AD patients exhibited decreased WC primarily in the γ band and in links related to frontal regions; while PD-D patients exhibited increased WC primarily in the α and β bands and in temporo-parietal links. Linear discriminant analysis (LDA) of RWE produced a maximum accuracy of 79.18% for diagnosing PD-D and 81.25% for diagnosing AD. The discriminant accuracy was 73.40% with 78.78% sensitivity and 69.47% specificity. In distinguishing between the two diseases; the maximum performance of LDA using WC was 80.19%. We suggest that using a wavelet approach to evaluate EEG results may facilitate discrimination between PD-D and AD. In particular; RWE is useful for differentiating individuals with and without dementia and WC is useful for differentiating between PD-D and AD. Full article

(This article belongs to the Special Issue Wavelets, Fractals and Information Theory I)

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647 KiB

Open AccessArticle

Cloud Entropy Management System Involving a Fractional Power

by Rabha W. Ibrahim, Hamid A. Jalab and Abdullah Gani

Entropy 2016, 18(1), 14; https://doi.org/10.3390/e18010014 - 29 Dec 2015

Cited by 12 | Viewed by 4975

Abstract

Cloud computing (CC) capacities deliver high quality, connected with demand services and service-oriented construction. Nevertheless, a cloud service (CS) is normally derived from numerous stages of facilities and concert features, which determine the value of the cloud service. Therefore, it is problematic for [...] Read more.

Cloud computing (CC) capacities deliver high quality, connected with demand services and service-oriented construction. Nevertheless, a cloud service (CS) is normally derived from numerous stages of facilities and concert features, which determine the value of the cloud service. Therefore, it is problematic for the users to estimate these cloud services and select them to appropriate their requirements. In this study, a new algorithm is carried out for a multi-agent system (MAS) based on fractional power. The study depends on a fractional difference equation of type two point boundary value problem (BVP) based on the fractional entropy. We discuss the existence of solutions for the system as well as the stability, utilizing the Hadamard well-posed problem. Experimental results show that the proposed method demonstrates stability and performance. Full article

(This article belongs to the Special Issue Complex and Fractional Dynamics)

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1121 KiB

Open AccessArticle

Improvement of the k-nn Entropy Estimator with Applications in Systems Biology

by Agata Charzyńska and Anna Gambin

Entropy 2016, 18(1), 13; https://doi.org/10.3390/e18010013 - 29 Dec 2015

Cited by 8 | Viewed by 6589

Abstract

In this paper, we investigate efficient estimation of differential entropy for multivariate random variables. We propose bias correction for the nearest neighbor estimator, which yields more accurate results in higher dimensions. In order to demonstrate the accuracy of the improvement, we calculated the [...] Read more.

In this paper, we investigate efficient estimation of differential entropy for multivariate random variables. We propose bias correction for the nearest neighbor estimator, which yields more accurate results in higher dimensions. In order to demonstrate the accuracy of the improvement, we calculated the corrected estimator for several families of random variables. For multivariate distributions, we considered the case of independent marginals and the dependence structure between the marginal distributions described by Gaussian copula. The presented solution may be particularly useful for high dimensional data, like those analyzed in the systems biology field. To illustrate such an application, we exploit differential entropy to define the robustness of biochemical kinetic models. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

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1169 KiB

Open AccessArticle

Wide Range Multiscale Entropy Changes through Development

by Nicola R. Polizzotto, Tetsuya Takahashi, Christopher P. Walker and Raymond Y. Cho

Entropy 2016, 18(1), 12; https://doi.org/10.3390/e18010012 - 29 Dec 2015

Cited by 10 | Viewed by 5678

Abstract

How variability in the brain’s neurophysiologic signals evolves during development is important for a global, system-level understanding of brain maturation and its disturbance in neurodevelopmental disorders. In the current study, we use multiscale entropy (MSE), a measure that has been related to signal [...] Read more.

How variability in the brain’s neurophysiologic signals evolves during development is important for a global, system-level understanding of brain maturation and its disturbance in neurodevelopmental disorders. In the current study, we use multiscale entropy (MSE), a measure that has been related to signal complexity, to investigate how this variability evolves during development across a broad range of temporal scales. We computed MSE, standard deviation (STD) and standard spectral analyses on resting EEG from 188 healthy individuals aged 8–22 years old. We found age-related increases in entropy at lower scales (<~20 ms) and decreases in entropy at higher scales (~60–80 ms). Decreases in the overall signal STD were anticorrelated with entropy, especially in the lower scales, where regression analyses showed substantial covariation of observed changes. Our findings document for the first time the scale dependency of developmental changes from childhood to early adulthood, challenging a parsimonious MSE-based account of brain maturation along a unidimensional, complexity measure. At the level of analysis permitted by electroencephalography (EEG), MSE could capture critical spatiotemporal variations in the role of noise in the brain. However, interpretations critically rely on defining how signal STD affects MSE properties. Full article

(This article belongs to the Special Issue Multiscale Entropy and Its Applications in Medicine and Biology)

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1106 KiB

Open AccessArticle

Effect of Magnetic Field on Entropy Generation in a Microchannel Heat Sink with Offset Fan Shaped

by Mohammad Nasiri, Mohammad Mehdi Rashidi and Giulio Lorenzini

Entropy 2016, 18(1), 10; https://doi.org/10.3390/e18010010 - 29 Dec 2015

Cited by 18 | Viewed by 6889

Abstract

In this study, convection flow in microchannel heat sink with offset fan-shaped reentrant cavities in sidewall filled with Fe₃O₄-water is numerically investigated. The effects of changing some parameters such as Reynolds number and magnetic field are considered. The nanofluid [...] Read more.

In this study, convection flow in microchannel heat sink with offset fan-shaped reentrant cavities in sidewall filled with Fe₃O₄-water is numerically investigated. The effects of changing some parameters such as Reynolds number and magnetic field are considered. The nanofluid flow is laminar, steady and incompressible, while the thermo-physical properties of nanoparticles were assumed constant. A finite volume method and two phase mixture models were used to simulate the flow. The obtained results show that the frictional entropy generation increases as Reynolds number increases, while a reverse trend is observed for thermal entropy generation. By applying a non-uniform magnetic field, the entropy generation due to heat transfer decreases at first and then increases. When using the uniform magnetic field, the frictional entropy generation and thermal entropy generation is negligible. For all studied cases, the total entropy generation decreases using non-uniform magnetic fields. The results indicate that by increasing the magnetic field power, the total entropy generation decreases. Full article

(This article belongs to the Special Issue Entropy in Nanofluids)

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Entropy, Volume 18, Issue 1 (January 2016) – 36 articles

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