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Entropy, Volume 20, Issue 1 (January 2018)

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Cover Story (view full-size image) Deltas are undergoing change due to natural and anthropogenic impacts, thus there is a need to [...] Read more.
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Open AccessArticle Macroscopic Internal Variables and Mesoscopic Theory: A Comparison Considering Liquid Crystals
Entropy 2018, 20(1), 81; https://doi.org/10.3390/e20010081
Received: 25 December 2017 / Revised: 15 January 2018 / Accepted: 16 January 2018 / Published: 22 January 2018
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Abstract
Internal and mesoscopic variables differ fundamentally from each other: both are state space variables, but mesoscopic variables are additionally equipped with a distribution function introducing a statistical item into consideration which is missing in connection with internal variables. Thus, the alignment tensor of
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Internal and mesoscopic variables differ fundamentally from each other: both are state space variables, but mesoscopic variables are additionally equipped with a distribution function introducing a statistical item into consideration which is missing in connection with internal variables. Thus, the alignment tensor of the liquid crystal theory can be introduced as an internal variable or as one generated by a mesoscopic background using the microscopic director as a mesoscopic variable. Because the mesoscopic variable is part of the state space, the corresponding balance equations change into mesoscopic balances, and additionally an evolution equation of the mesoscopic distribution function appears. The flexibility of the mesoscopic concept is not only demonstrated for liquid crystals, but is also discussed for dipolar media and flexible fibers. Full article
(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)
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Open AccessArticle Entanglement Entropy of the Spin-1 Condensates at Zero Temperature
Entropy 2018, 20(1), 80; https://doi.org/10.3390/e20010080
Received: 14 December 2017 / Revised: 10 January 2018 / Accepted: 18 January 2018 / Published: 22 January 2018
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Abstract
For spin-1 condensates, the spatial degrees of freedom can be considered as being frozen at temperature zero, while the spin-degrees of freedom remain free. Under this condition, the entanglement entropy has been derived exactly with an analytical form. The entanglement entropy is found
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For spin-1 condensates, the spatial degrees of freedom can be considered as being frozen at temperature zero, while the spin-degrees of freedom remain free. Under this condition, the entanglement entropy has been derived exactly with an analytical form. The entanglement entropy is found to decrease monotonically with the increase of the magnetic polarization as expected. However, for the ground state in polar phase, an extremely steep fall of the entropy is found when the polarization emerges from zero. Then the fall becomes a gentle descent after the polarization exceeds a turning point. Full article
(This article belongs to the Special Issue Residual Entropy and Nonequilibrium States)
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Open AccessArticle A Newly Secure Solution to MIMOME OFDM-Based SWIPT Frameworks: A Two-Stage Stackelberg Game for a Multi-User Strategy
Entropy 2018, 20(1), 79; https://doi.org/10.3390/e20010079
Received: 22 December 2017 / Revised: 9 January 2018 / Accepted: 18 January 2018 / Published: 22 January 2018
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Abstract
The paper technically proposes a newly secure scheme for simultaneous wireless power and information transfer (SWIPT) frameworks. We take into account an orthogonal frequency division multiplexing (OFDM)-based game which is in relation to a multi-input multi-output multi-antenna Eavesdropper (MIMOME) strategy. The transceiver is
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The paper technically proposes a newly secure scheme for simultaneous wireless power and information transfer (SWIPT) frameworks. We take into account an orthogonal frequency division multiplexing (OFDM)-based game which is in relation to a multi-input multi-output multi-antenna Eavesdropper (MIMOME) strategy. The transceiver is generally able to witness the case imperfect channel state information (ICSI) at the transmitter side. Transferring power and information are conducted via orthogonally provided sub-carriers. We propose a two-step Stackelberg game to optimise the Utility Functions of both power and information parts. The price for the first stage (in connection with information) is the total power of the other sub-carriers over which the energy is supported. In this stage, the sum secrecy rate should be essentially maximised. The second level of the proposed Stackelberg game is in association with the energy part. In this stage, the price essentially is the total power of the other sub-carriers over which the information is transferred. In this stage, additionally, the total power transferred is fundamentally maximised. Subsequently, the optimally and near-optimally mathematical solutions are derived, for some special cases such as ICSI one. Finally, the simulations validate our scheme as well, authenticating our contribution’s tightness and efficiency. Full article
(This article belongs to the Section Information Theory)
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Open AccessArticle Anomalous Advection-Dispersion Equations within General Fractional-Order Derivatives: Models and Series Solutions
Entropy 2018, 20(1), 78; https://doi.org/10.3390/e20010078
Received: 3 November 2017 / Revised: 18 January 2018 / Accepted: 19 January 2018 / Published: 22 January 2018
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Abstract
In this paper, an anomalous advection-dispersion model involving a new general Liouville–Caputo fractional-order derivative is addressed for the first time. The series solutions of the general fractional advection-dispersion equations are obtained with the aid of the Laplace transform. The results are given to
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In this paper, an anomalous advection-dispersion model involving a new general Liouville–Caputo fractional-order derivative is addressed for the first time. The series solutions of the general fractional advection-dispersion equations are obtained with the aid of the Laplace transform. The results are given to demonstrate the efficiency of the proposed formulations to describe the anomalous advection dispersion processes. Full article
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory III)
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Open AccessArticle Using Entropy in Web Usage Data Preprocessing
Entropy 2018, 20(1), 67; https://doi.org/10.3390/e20010067
Received: 30 November 2017 / Revised: 10 January 2018 / Accepted: 13 January 2018 / Published: 22 January 2018
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Abstract
The paper is focused on an examination of the use of entropy in the field of web usage mining. Entropy creates an alternative possibility of determining the ratio of auxiliary pages in the session identification using the Reference Length method. The experiment was
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The paper is focused on an examination of the use of entropy in the field of web usage mining. Entropy creates an alternative possibility of determining the ratio of auxiliary pages in the session identification using the Reference Length method. The experiment was conducted on two different web portals. The first log file was obtained from a course of virtual learning environment web portal. The second log file was received from the web portal with anonymous access. A comparison of the results of entropy estimation of the ratio of auxiliary pages and a sitemap estimation of the ratio of auxiliary pages showed that in the case of sitemap abundance, entropy could be a full-valued substitution for the estimate of the ratio of auxiliary pages. Full article
(This article belongs to the Special Issue Entropy-based Data Mining)
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Open AccessArticle Adaptive Diagnosis for Rotating Machineries Using Information Geometrical Kernel-ELM Based on VMD-SVD
Entropy 2018, 20(1), 73; https://doi.org/10.3390/e20010073
Received: 6 December 2017 / Revised: 14 January 2018 / Accepted: 16 January 2018 / Published: 21 January 2018
Cited by 2 | PDF Full-text (18367 KB) | HTML Full-text | XML Full-text
Abstract
Rotating machineries often work under severe and variable operation conditions, which brings challenges to fault diagnosis. To deal with this challenge, this paper discusses the concept of adaptive diagnosis, which means to diagnose faults under variable operation conditions with self-adaptively and little prior
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Rotating machineries often work under severe and variable operation conditions, which brings challenges to fault diagnosis. To deal with this challenge, this paper discusses the concept of adaptive diagnosis, which means to diagnose faults under variable operation conditions with self-adaptively and little prior knowledge or human intervention. To this end, a novel algorithm is proposed, information geometrical extreme learning machine with kernel (IG-KELM). From the perspective of information geometry, the structure and Riemannian metric of Kernel-ELM is specified. Based on the geometrical structure, an IG-based conformal transformation is created to improve the generalization ability and self-adaptability of KELM. The proposed IG-KELM, in conjunction with variation mode decomposition (VMD) and singular value decomposition (SVD) is utilized for adaptive diagnosis: (1) VMD, as a new self-adaptive signal processing algorithm is used to decompose the raw signals into several intrinsic mode functions (IMFs). (2) SVD is used to extract the intrinsic characteristics from the matrix constructed with IMFs. (3) IG-KELM is used to diagnose faults under variable conditions self-adaptively with no requirement of prior knowledge or human intervention. Finally, the proposed method was applied on fault diagnosis of a bearing and hydraulic pump. The results show that the proposed method outperforms the conventional method by up to 7.25% and 7.78% respectively, in percentages of accuracy. Full article
(This article belongs to the Section Information Theory)
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Open AccessFeature PaperArticle Characterizing Normal and Pathological Gait through Permutation Entropy
Entropy 2018, 20(1), 77; https://doi.org/10.3390/e20010077
Received: 10 November 2017 / Revised: 15 January 2018 / Accepted: 16 January 2018 / Published: 19 January 2018
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Abstract
Cerebral palsy is a physical impairment stemming from a brain lesion at perinatal time, most of the time resulting in gait abnormalities: the first cause of severe disability in childhood. Gait study, and instrumental gait analysis in particular, has been receiving increasing attention
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Cerebral palsy is a physical impairment stemming from a brain lesion at perinatal time, most of the time resulting in gait abnormalities: the first cause of severe disability in childhood. Gait study, and instrumental gait analysis in particular, has been receiving increasing attention in the last few years, for being the complex result of the interactions between different brain motor areas and thus a proxy in the understanding of the underlying neural dynamics. Yet, and in spite of its importance, little is still known about how the brain adapts to cerebral palsy and to its impaired gait and, consequently, about the best strategies for mitigating the disability. In this contribution, we present the hitherto first analysis of joint kinematics data using permutation entropy, comparing cerebral palsy children with a set of matched control subjects. We find a significant increase in the permutation entropy for the former group, thus indicating a more complex and erratic neural control of joints and a non-trivial relationship between the permutation entropy and the gait speed. We further show how this information theory measure can be used to train a data mining model able to forecast the child’s condition. We finally discuss the relevance of these results in clinical applications and specifically in the design of personalized medicine interventions. Full article
(This article belongs to the Special Issue Information Theory Applied to Physiological Signals)
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Open AccessArticle Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series
Entropy 2018, 20(1), 76; https://doi.org/10.3390/e20010076
Received: 8 December 2017 / Revised: 14 January 2018 / Accepted: 16 January 2018 / Published: 19 January 2018
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Abstract
This work is focused on latent-variable graphical models for multivariate time series. We show how an algorithm which was originally used for finding zeros in the inverse of the covariance matrix can be generalized such that to identify the sparsity pattern of the
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This work is focused on latent-variable graphical models for multivariate time series. We show how an algorithm which was originally used for finding zeros in the inverse of the covariance matrix can be generalized such that to identify the sparsity pattern of the inverse of spectral density matrix. When applied to a given time series, the algorithm produces a set of candidate models. Various information theoretic (IT) criteria are employed for deciding the winner. A novel IT criterion, which is tailored to our model selection problem, is introduced. Some options for reducing the computational burden are proposed and tested via numerical examples. We conduct an empirical study in which the algorithm is compared with the state-of-the-art. The results are good, and the major advantage is that the subjective choices made by the user are less important than in the case of other methods. Full article
(This article belongs to the Section Information Theory)
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Open AccessArticle Finite-Time Thermodynamic Modeling and a Comparative Performance Analysis for Irreversible Otto, Miller and Atkinson Cycles
Entropy 2018, 20(1), 75; https://doi.org/10.3390/e20010075
Received: 3 December 2017 / Revised: 14 January 2018 / Accepted: 16 January 2018 / Published: 19 January 2018
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Abstract
Finite-time thermodynamic models for an Otto cycle, an Atkinson cycle, an over-expansion Miller cycle (M1), an LIVC Miller cycle through late intake valve closure (M2) and an LIVC Miller cycle with constant compression ratio (M3) have been established. The models for the two
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Finite-time thermodynamic models for an Otto cycle, an Atkinson cycle, an over-expansion Miller cycle (M1), an LIVC Miller cycle through late intake valve closure (M2) and an LIVC Miller cycle with constant compression ratio (M3) have been established. The models for the two LIVC Miller cycles are first developed; and the heat-transfer and friction losses are considered with the effects of real engine parameters. A comparative analysis for the energy losses and performances has been conducted. The optimum compression-ratio ranges for the efficiency and effective power are different. The comparative results of cycle performances are influenced together by the ratios of the energy losses and the cycle types. The Atkinson cycle has the maximum peak power and efficiency, but the minimum power density; and the M1 cycle can achieve the optimum comprehensive performances. The less net fuel amount and the high peak cylinder pressure (M3 cycle) have a significantly adverse effect on the loss ratios of the heat-transfer and friction of the M2 and M3 cycles; and the effective power and energy efficiency are always lower than the M1 and Atkinson cycles. When greatly reducing the weights of the heat-transfer and friction, the M3 cycle has significant advantage in the energy efficiency. The results obtained can provide guidance for selecting the cycle type and optimizing the performances of a real engine. Full article
(This article belongs to the Section Thermodynamics)
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Open AccessReview Constructal Optimizations for Heat and Mass Transfers Based on the Entransy Dissipation Extremum Principle, Performed at the Naval University of Engineering: A Review
Entropy 2018, 20(1), 74; https://doi.org/10.3390/e20010074
Received: 18 December 2017 / Revised: 13 January 2018 / Accepted: 16 January 2018 / Published: 19 January 2018
Cited by 2 | PDF Full-text (6335 KB) | HTML Full-text | XML Full-text
Abstract
Combining entransy theory with constructal theory, this mini-review paper summarizes the constructal optimization work of heat conduction, convective heat transfer, and mass transfer problems during the authors’ working time in the Naval University of Engineering. The entransy dissipation extremum principle (EDEP) is applied
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Combining entransy theory with constructal theory, this mini-review paper summarizes the constructal optimization work of heat conduction, convective heat transfer, and mass transfer problems during the authors’ working time in the Naval University of Engineering. The entransy dissipation extremum principle (EDEP) is applied in constructal optimizations, and this paper is divided into three parts. The first part is constructal entransy dissipation rate minimizations of heat conduction and finned cooling problems. It includes constructal optimization for a “volume-to-point” heat-conduction assembly with a tapered element, constructal optimizations for “disc-to-point” heat-conduction assemblies with the premise of an optimized last-order construct and without this premise, and constructal optimizations for four kinds of fin assemblies: T-, Y-, umbrella-, and tree-shaped fins. The second part is constructal entransy dissipation rate minimizations of cooling channel and steam generator problems. It includes constructal optimizations for heat generating volumes with tree-shaped and parallel channels, constructal optimization for heat generating volume cooled by forced convection, and constructal optimization for a steam generator. The third part is constructal entransy dissipation rate minimizations of mass transfer problems. It includes constructal optimizations for “volume-to-point” rectangular assemblies with constant and tapered channels, and constructal optimizations for “disc-to-point” assemblies with the premise of an optimized last-order construct and without this premise. The results of the three parts show that the mean heat transfer temperature differences of the heat conduction assemblies are not always decreased when their internal complexity increases. The average heat transfer rate of the steam generator obtained by entransy dissipation rate maximization is increased by 58.7% compared with that obtained by heat transfer rate maximization. Compared with the rectangular mass transfer assembly with a constant high permeability pathway (HPP), the maximum pressure drops of the element and first-order assembly with tapered HPPs are decreased by 6% and 11%, respectively. The global transfer performances of the transfer bodies are improved after optimizations, and new design guidelines derived by EDEP, which are different from the conventional optimization objectives, are provided. Full article
(This article belongs to the Section Thermodynamics)
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Open AccessArticle Non-Gaussian Closed Form Solutions for Geometric Average Asian Options in the Framework of Non-Extensive Statistical Mechanics
Entropy 2018, 20(1), 71; https://doi.org/10.3390/e20010071
Received: 17 November 2017 / Revised: 30 December 2017 / Accepted: 16 January 2018 / Published: 18 January 2018
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Abstract
In this paper we consider pricing problems of the geometric average Asian options under a non-Gaussian model, in which the underlying stock price is driven by a process based on non-extensive statistical mechanics. The model can describe the peak and fat tail characteristics
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In this paper we consider pricing problems of the geometric average Asian options under a non-Gaussian model, in which the underlying stock price is driven by a process based on non-extensive statistical mechanics. The model can describe the peak and fat tail characteristics of returns. Thus, the description of underlying asset price and the pricing of options are more accurate. Moreover, using the martingale method, we obtain closed form solutions for geometric average Asian options. Furthermore, the numerical analysis shows that the model can avoid underestimating risks relative to the Black-Scholes model. Full article
(This article belongs to the Special Issue Nonadditive Entropies and Complex Systems)
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Open AccessArticle An Operation Reduction Using Fast Computation of an Iteration-Based Simulation Method with Microsimulation-Semi-Symbolic Analysis
Entropy 2018, 20(1), 62; https://doi.org/10.3390/e20010062
Received: 24 October 2017 / Revised: 26 December 2017 / Accepted: 11 January 2018 / Published: 18 January 2018
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Abstract
This paper presents a method for shortening the computation time and reducing the number of math operations required in complex calculations for the analysis, simulation, and design of processes and systems. The method is suitable for education and engineering applications. The efficacy of
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This paper presents a method for shortening the computation time and reducing the number of math operations required in complex calculations for the analysis, simulation, and design of processes and systems. The method is suitable for education and engineering applications. The efficacy of the method is illustrated with a case study of a complex wireless communication system. The computer algebra system (CAS) was applied to formulate hypotheses and define the joint probability density function of a certain modulation technique. This innovative method was used to prepare microsimulation-semi-symbolic analyses to fully specify the wireless system. The development of an iteration-based simulation method that provides closed form solutions is presented. Previously, expressions were solved using time-consuming numerical methods. Students can apply this method for performance analysis and to understand data transfer processes. Engineers and researchers may use the method to gain insight into the impact of the parameters necessary to properly transmit and detect information, unlike traditional numerical methods. This research contributes to this field by improving the ability to obtain closed form solutions of the probability density function, outage probability, and considerably improves time efficiency with shortened computation time and reducing the number of calculation operations. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle Energetic and Exergetic Analysis of a Transcritical N2O Refrigeration Cycle with an Expander
Entropy 2018, 20(1), 31; https://doi.org/10.3390/e20010031
Received: 6 December 2017 / Revised: 31 December 2017 / Accepted: 4 January 2018 / Published: 18 January 2018
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Abstract
Comparative energy and exergy investigations are reported for a transcritical N2O refrigeration cycle with a throttling valve or with an expander when the gas cooler exit temperature varies from 30 to 55 °C and the evaporating temperature varies from −40 to
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Comparative energy and exergy investigations are reported for a transcritical N2O refrigeration cycle with a throttling valve or with an expander when the gas cooler exit temperature varies from 30 to 55 °C and the evaporating temperature varies from −40 to 10 °C. The system performance is also compared with that of similar cycles using CO2. Results show that the N2O expander cycle exhibits a larger maximum cooling coefficient of performance (COP) and lower optimum discharge pressure than that of the CO2 expander cycle and N2O throttling valve cycle. It is found that in the N2O throttling valve cycle, the irreversibility of the throttling valve is maximum and the exergy losses of the gas cooler and compressor are ordered second and third, respectively. In the N2O expander cycle, the largest exergy loss occurs in the gas cooler, followed by the compressor and the expander. Compared with the CO2 expander cycle and N2O throttling valve cycle, the N2O expander cycle has the smallest component-specific exergy loss and the highest exergy efficiency at the same operating conditions and at the optimum discharge pressure. It is also proven that the maximum COP and the maximum exergy efficiency cannot be obtained at the same time for the investigated cycles. Full article
(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)
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Open AccessArticle The Fractality of Polar and Reed–Muller Codes
Entropy 2018, 20(1), 70; https://doi.org/10.3390/e20010070
Received: 16 October 2017 / Revised: 10 January 2018 / Accepted: 15 January 2018 / Published: 17 January 2018
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Abstract
The generator matrices of polar codes and Reed–Muller codes are submatrices of the Kronecker product of a lower-triangular binary square matrix. For polar codes, the submatrix is generated by selecting rows according to their Bhattacharyya parameter, which is related to the error probability
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The generator matrices of polar codes and Reed–Muller codes are submatrices of the Kronecker product of a lower-triangular binary square matrix. For polar codes, the submatrix is generated by selecting rows according to their Bhattacharyya parameter, which is related to the error probability of sequential decoding. For Reed–Muller codes, the submatrix is generated by selecting rows according to their Hamming weight. In this work, we investigate the properties of the index sets selecting those rows, in the limit as the blocklength tends to infinity. We compute the Lebesgue measure and the Hausdorff dimension of these sets. We furthermore show that these sets are finely structured and self-similar in a well-defined sense, i.e., they have properties that are common to fractals. Full article
(This article belongs to the Section Information Theory)
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Open AccessArticle An Entropic Model for the Assessment of Streamwise Velocity Dip in Wide Open Channels
Entropy 2018, 20(1), 69; https://doi.org/10.3390/e20010069
Received: 31 October 2017 / Revised: 5 January 2018 / Accepted: 13 January 2018 / Published: 17 January 2018
Cited by 3 | PDF Full-text (7227 KB) | HTML Full-text | XML Full-text
Abstract
The three-dimensional structure of river flow and the presence of secondary currents, mainly near walls, often cause the maximum cross-sectional velocity to occur below the free surface, which is known as the “dip” phenomenon. The present study proposes a theoretical model derived from
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The three-dimensional structure of river flow and the presence of secondary currents, mainly near walls, often cause the maximum cross-sectional velocity to occur below the free surface, which is known as the “dip” phenomenon. The present study proposes a theoretical model derived from the entropy theory to predict the velocity dip position along with the corresponding velocity value. Field data, collected at three ungauged sections located along the Alzette river in the Grand Duchy of Luxembourg and at three gauged sections located along three large rivers in Basilicata (southern Italy), were used to test its validity. The results show that the model is in good agreement with the experimental measurements and, when compared with other models documented in the literature, yields the least percentage error. Full article
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