Entropy, Volume 17, Issue 12 (December 2015) – 33 articles

The spontaneous violation of Lorentz and diffeomorphism invariance in a phase near the big bang lowers the entropy, allowing for an arrow of time and the second law of thermodynamics. The spontaneous symmetry breaking leads to O(3,1) → O(3) × R , where O(3) is the rotational symmetry of the Friedmann–Lemaître–Robertson–Walker spacetime. The Weyl curvature tensor C_μνρσ vanishes in the FLRW spacetime satisfying the Penrose zero Weyl curvature conjecture. The requirement of a measure of gravitational entropy is discussed. The vacuum expectation value 〈0|ψ_μ|0〉 ≠ 0 for a vector field ψ_μ acts as an order parameter and at the critical temperature T_c a phase transition occurs breaking the Lorentz symmetry spontaneously. During the ordered O(3) symmetry phase the entropy is vanishingly small and for T < T_c as the universe expands the anti-restored O(3,1) Lorentz symmetry leads to a disordered phase and a large increase in entropy creating the arrow of time. Full article

In generalizing the special-relativistic one-component version of Eckart’s continuum thermodynamics to general-relativistic space-times with Riemannian or post-Riemannian geometry as presented by Schouten (Schouten, J.A. Ricci-Calculus, 1954) and Blagojevic (Blagojevic, M. Gauge Theories of Gravitation, 2013) we consider the entropy production and other thermodynamical quantities, such as the entropy flux and the Gibbs fundamental equation. We discuss equilibrium conditions in gravitational theories, which are based on such geometries. In particular, thermodynamic implications of the non-symmetry of the energy-momentum tensor and the related spin balance equations are investigated, also for the special case of general relativity. Full article

We consider the independent sum of a given random variable with a Gaussian variable and an infinitely divisible one. We find a novel tight upper bound on the entropy of the sum which still holds when the variable possibly has an infinite second moment. The proven bound has several implications on both information theoretic problems and infinitely divisible noise channels’ transmission rates. Full article

The fractional-order hyperchaotic Lorenz system is solved as a discrete map by applying the Adomian decomposition method (ADM). Lyapunov Characteristic Exponents (LCEs) of this system are calculated according to this deduced discrete map. Complexity of this system versus parameters are analyzed by LCEs, bifurcation diagrams, phase portraits, complexity algorithms. Results show that this system has rich dynamical behaviors. Chaos and hyperchaos can be generated by decreasing fractional order q in this system. It also shows that the system is more complex when q takes smaller values. SE and C 0 complexity algorithms provide a parameter choice criteria for practice applications of fractional-order chaotic systems. The fractional-order system is implemented by digital signal processor (DSP), and a pseudo-random bit generator is designed based on the implemented system, which passes the NIST test successfully. Full article

This comment by the author discusses paragraph 3.3. Adiabatic Phenomena—An Analogy of the published article [1]. The paragraph draws an incorrect analogy between Maxwellian gases such as found in the atmosphere, and non-Maxwellian gases embodied, for example, by electrical carriers in thermoelectric materials. As reported by the author in more recent articles, Maxwellian gases do not produce spontaneous temperature gradients in the presence of a force field. However, non-Maxwellian gases, such as Fermions or Bosons, can produce such gradients. Full article

Aim: To detect pathological brain conditions early is a core procedure for patients so as to have enough time for treatment. Traditional manual detection is either cumbersome, or expensive, or time-consuming. We aim to offer a system that can automatically identify pathological brain images in this paper. Method: We propose a novel image feature, viz., Fractional Fourier Entropy (FRFE), which is based on the combination of Fractional Fourier Transform (FRFT) and Shannon entropy. Afterwards, the Welch’s t-test (WTT) and Mahalanobis distance (MD) were harnessed to select distinguishing features. Finally, we introduced an advanced classifier: twin support vector machine (TSVM). Results: A 10 × K-fold stratified cross validation test showed that this proposed “FRFE + WTT + TSVM” yielded an accuracy of 100.00%, 100.00%, and 99.57% on datasets that contained 66, 160, and 255 brain images, respectively. Conclusions: The proposed “FRFE + WTT + TSVM” method is superior to 20 state-of-the-art methods. Full article

In this study, we have applied the modified exp(−Ω(ξ))-expansion function method to the (2 + 1)-dimensional Boussinesq water equation. We have obtained some new analytical solutions such as exponential function, complex function and hyperbolic function solutions. It has been observed that all analytical solutions have been verified to the (2 + 1)-dimensional Boussinesq water equation by using Wolfram Mathematica 9. We have constructed the two- and three-dimensional surfaces for all analytical solutions obtained in this paper using the same computer program. Full article

As a native scheme to evaluate hydrodynamic force in the lattice Boltzmann method, the momentum exchange method has some excellent features, such as simplicity, accuracy, high efficiency and easy parallelization. Especially, it is independent of boundary geometry, preventing from solving the Navier–Stokes equations on complex boundary geometries in the boundary-integral methods. We review the origination and main developments of the momentum exchange method in lattice Boltzmann simulations. Then several practical techniques to fill newborn fluid nodes are discussed for the simulations of fluid-structure interactions. Finally, some representative applications show the wide applicability of the momentum exchange method, such as movements of rigid particles, interactions of deformation particles, particle suspensions in turbulent flow and multiphase flow, etc. Full article

In this paper a simplified two-dimensional computational model for studying the entropy generation characteristics of thermoacoustic heat exchangers with plane fins is presented. The model integrates the equations of the standard linear thermoacoustic theory into an energy balance-based numerical calculus scheme. Relevant computation results are the spatial distribution of the time-averaged temperature, heat fluxes and entropy generation rates within a channel of a parallel-plate stack and adjoining heat exchangers. For a thermoacoustic device working in the refrigeration mode, this study evidences as a target refrigeration output level can be achieved selecting simultaneously the heat exchangers fin length and fin interspacing for minimum entropy generation and that the resulting configuration is a point of maximum coefficient of performance. The proposed methodology, when extended to other configurations, could be used as a viable design tool for heat exchangers in thermoacoustic applications. Full article

The graph entropies inspired by Shannon’s entropy concept become the information-theoretic quantities for measuring the structural information of graphs and complex networks. In this paper, we continue studying some new properties of the graph entropies based on information functionals involving vertex degrees. We prove the monotonicity of the graph entropies with respect to the power exponent. Considering only the maximum and minimum degrees of the ( n , m ) -graph, we obtain some upper and lower bounds for the degree-based graph entropy. These bounds have different performances to restrict the degree-based graph entropy in different kinds of graphs. Moreover the degree-based graph entropy can be estimated by these bounds. Full article

In this paper, we generalize the permutation entropy (PE) measure to binary sequences, which is based on Shannon’s entropy, and theoretically analyze this measure for random binary sequences. We deduce the theoretical value of PE for random binary sequences, which can be used to measure the randomness of binary sequences. We also reveal the relationship between this PE measure with other randomness measures, such as Shannon’s entropy and Lempel–Ziv complexity. The results show that PE is consistent with these two measures. Furthermore, we use PE as one of the randomness measures to evaluate the randomness of chaotic binary sequences. Full article

The present paper analyzes numerically the entropy generation induced by forced convection in a canonical configuration. The configuration itself includes two well known fluid dynamic problems: (1) an external flow (flow around a cylinder, Kármán flow); and (2) an internal flow (flow between two concentric rotating cylinders, Couette flow). In many daily engineering issues (e.g., cooling of electric machines), a combination of these problems occurs and has to be investigated. Using the canonical configuration, the fields of entropy generation are analyzed in this work for a constant wall heat flux but varying two key parameters (Reynolds numbers Re_∞ and Re₀). The entropy generation due to conduction shows an absolute minimum around Re₀ = 10,000. The same minima can be found by a detailed analysis of the temperature profile. Thus, entropy generation seems to be a suitable indicator for optimizing heat exchange processes and delivers a large amount of information concerning fluid and heat transport. Full article

We give a review, in the style of an essay, of the author’s 1998 matter-gravity entanglement hypothesis which, unlike the standard approach to entropy based on coarse-graining, offers a definition for the entropy of a closed system as a real and objective quantity. We explain how this approach offers an explanation for the Second Law of Thermodynamics in general and a non-paradoxical understanding of information loss during black hole formation and evaporation in particular. It also involves a radically different from usual description of black hole equilibrium states in which the total state of a black hole in a box together with its atmosphere is a pure state—entangled in just such a way that the reduced state of the black hole and of its atmosphere are each separately approximately thermal. We also briefly recall some recent work of the author which involves a reworking of the string-theory understanding of black hole entropy consistent with this alternative description of black hole equilibrium states and point out that this is free from some unsatisfactory features of the usual string theory understanding. We also recall the author’s recent arguments based on this alternative description which suggest that the Anti de Sitter space (AdS)/conformal field theory (CFT) correspondence is a bijection between the boundary CFT and just the matter degrees of freedom of the bulk theory. Full article

Naval surface ships should use thermally driven heating and cooling technologies to continue the Navy’s leadership role in protecting the marine environment. Steam ejector refrigeration (SER) or steam ejector heat pump (SEHP) systems are thermally driven heating and cooling technologies and seem to be a promising technology to reduce emissions for heating and cooling on board naval surface ships. In this study, design and thermodynamic analysis of a seawater cooled SER and SEHP as an HVAC system for a naval surface ship application are presented and compared with those of a current typical naval ship system case, an H₂O-LiBr absorption heat pump and a vapour-compression heat pump. The off-design study estimated the coefficient of performances (COPs) were 0.29–0.11 for the cooling mode and 1.29–1.11 for the heating mode, depending on the pressure of the exhaust gas boiler at off-design conditions. In the system operating at the exhaust gas boiler pressure of 0.2 MPa, the optimum area ratio obtained was 23.30. Full article

Current brain-age prediction methods using magnetic resonance imaging (MRI) attempt to estimate the physiological brain age via some kind of machine learning of chronological brain age data to perform the classification task. Such a predictive approach imposes greater risk of either over-estimate or under-estimate, mainly due to limited training data. A new conceptual framework for more reliable MRI-based brain-age prediction is by systematic brain-age grouping via the implementation of the phylogenetic tree reconstruction and measures of information complexity. Experimental results carried out on a public MRI database suggest the feasibility of the proposed concept. Full article

A divergence function on a manifold M defines a Riemannian metric g and dually coupled affine connections ∇ and ∇ * on M. When M is dually flat, that is flat with respect to ∇ and ∇ * , a canonical divergence is known, which is uniquely determined from ( M , g , ∇ , ∇ * ) . We propose a natural definition of a canonical divergence for a general, not necessarily flat, M by using the geodesic integration of the inverse exponential map. The new definition of a canonical divergence reduces to the known canonical divergence in the case of dual flatness. Finally, we show that the integrability of the inverse exponential map implies the geodesic projection property. Full article

To explore information hidden in the electromyographic (EMG) signals of the urethral sphincter that may be of prognostic significance for patients with primary bladder neck obstruction (PBNO), 41 patients with voiding difficulty were divided into four groups: 1) patients with primary bladder neck obstruction (PBNO) with successful (Group 1, n = 14) and 2) unsuccessful (Group 2, n = 8) surgical outcomes, 3) patients with detrusor overactivity (Group 3, n = 7), and 4) patients with detrusor-external sphincter dyssynergia (Group 4, n = 12). All patients underwent baseline urodynamic studies (preoperative for Group 1 and Group 2) for comparison. The results demonstrated that, despite no significant difference in urodynamic parameters between Group 1 and Group 2, the large-scale multiscale entropy (MSE) of preoperative EMG (i.e., MSE_LS(EMG)) of Group 1 was significantly higher than that of Group 2 without notable difference between Group 1 and Group 3 (i.e., patients with normal sphincter function). Moreover, the MSE_LS(EMG) and small-scale MSE of preoperative EMG (i.e., MSE_SS(EMG)) of Group 2 were notably higher than those of Group 4 (i.e., patients with abnormal sphincter function), while both MSE_LS(EMG) and MSE_SS(EMG) of Group 3 were notably higher than those of Group 2. In conclusion, using MSE analysis for assessing preoperative urethral sphincter EMG signals successfully distinguished between PBNO patients with subsequent successful surgery from those with surgical failure possibly due to subtle functional impairment of the urethral sphincter that cannot be detected by routine urodynamic studies. The results, therefore, highlight the potential clinical significance of this analytical tool in guiding urologists regarding their choice of medical versus surgical treatment for this patient population. Full article

Earlier investment practices show that there lies a discrepancy between the actual fund strategy and stated fund strategy. Using a minimum spanning tree (MST) and planar maximally-filtered graph (PMFG), we build a network of open-ended funds in China’s market and investigate the evolution characteristics of the networks over multiple time periods and timescales. The evolution characteristics, especially the locations of clustering central nodes, show that the actual strategy of the open-ended funds in China’s market significantly differs from the original stated strategy. When the investment horizon and timescale extend, the funds approach an identical actual strategy. This work introduces a novel network-based quantitative method to help investors identify the actual strategy of open-ended funds. Full article

We study the extended phase space thermodynamics for hairy AdS black hole solutions to Einstein-Maxwell-Λ theory conformally coupled to a scalar field in five dimensions. We find these solutions to exhibit van der Waals behaviour in both the charged/uncharged cases, and reentrant phase transitions in the charged case. This is the first example of reentrant phase transitions in a five dimensional gravitational system which does not include purely gravitational higher curvature corrections. Full article

In this paper, we proposed a novel information-based approach to precision analysis of indoor wireless local area network (WLAN) localization using location fingerprint. First of all, by using the Fisher information matrix (FIM), we derive the fundamental limit of WLAN fingerprint-based localization precision considering different signal distributions in characterizing the variation of received signal strengths (RSSs) in the target environment. After that, we explore the relationship between the localization precision and access point (AP) placement, which can provide valuable suggestions for the design of the highly-precise localization system. Second, we adopt the heuristic simulated annealing (SA) algorithm to optimize the AP locations for the sake of approaching the fundamental limit of localization precision. Finally, the extensive simulations and experiments are conducted in both regular line-of-sight (LOS) and irregular non-line-of-sight (NLOS) environments to demonstrate that the proposed approach can not only effectively improve the WLAN fingerprint-based localization precision, but also reduce the time overhead. Full article

A recent work reported a local stability analysis of a thermo-economical model of an irreversible heat engine working under maximum power conditions. That work showed that after small perturbations to the working temperatures, the system decreases exponentially to the steady state characterized by two different relaxation times. This work extends the local stability analysis considering other performance regimes: the Maximum Efficient Power (MEP) and the Ecological Function (EF) regimes. The relaxation time was shown under different performance regimes as functions of the temperature ratio τ = T₂/T₁, with T₁ > T₂, the fractional fuel cost f and a lumped parameter R related to the internal irreversibilities degree. Under Maximum Efficient Power conditions the relaxation times are less than the relaxation times under both Maximum Ecological function and Maximum Power. At Maximum Power Efficient conditions, the model gives better stability conditions than for the other two regimes. Full article

Nature’s many complex systems—physical, biological, and cultural—are islands of low-entropy order within increasingly disordered seas of surrounding, high-entropy chaos. Energy is a principal facilitator of the rising complexity of all such systems in the expanding Universe, including galaxies, stars, planets, life, society, and machines. A large amount of empirical evidence—relating neither entropy nor information, rather energy—suggests that an underlying simplicity guides the emergence and growth of complexity among many known, highly varied systems in the 14-billion-year-old Universe, from big bang to humankind. Energy flows are as centrally important to life and society as they are to stars and galaxies. In particular, the quantity energy rate density—the rate of energy flow per unit mass—can be used to explicate in a consistent, uniform, and unifying way a huge collection of diverse complex systems observed throughout Nature. Operationally, those systems able to utilize optimal amounts of energy tend to survive and those that cannot are non-randomly eliminated. Full article

In this paper we develop a new procedure for entropic image edge detection. The presented method computes the Jensen–Shannon divergence of the normalized grayscale histogram of a set of multi-sized double sliding windows over the entire image. The procedure presents a good performance in images with textures, contrast variations and noise. We illustrate our procedure in the edge detection of medical images. Full article

Long-memory processes, in particular fractional Gaussian noise processes, have been applied as models for many phenomena occurring in nature. Non-stationarities, such as trends, mean level-shifts, etc., impact the accuracy of long-memory parameter estimators, giving rise to biases and misinterpretations of the phenomena. In this article, a novel methodology for the detection and location of mean level-shifts in stationary long-memory fractional Gaussian noise (fGn) signals is proposed. It is based on a joint application of the wavelet-Tsallis q-entropy as a preprocessing technique and a peak detection methodology. Extensive simulation experiments in synthesized fGn signals with mean level-shifts confirm that the proposed methodology not only detects, but also locates level-shifts with high accuracy. A comparative study against standard techniques of level-shift detection and location shows that the technique based on wavelet-Tsallis q-entropy outperforms the one based on trees and the Bai and Perron procedure, as well. Full article

This article discusses the peculiarities of self-organization behavior and formation of dissipative structures during friction of antifriction alloys for slide bearings against a steel counterbody. It shows that during self-organization, the moment of friction in a tribosystem may be decreasing with the load growth and in the bifurcations of the coefficient of friction with respect to load. Self-organization and the formation of dissipative structures lead to an increase in the seizure load. Full article

This paper proposes a novel image watermarking method based on local energy and maximum entropy aiming to improve the robustness. First, the image feature distribution is extracted by employing the local energy model and then it is transformed as a digital watermark by employing a Discrete Cosine Transform (DCT). An offset image is thus obtained according to the difference between the extracted digital watermarking and the feature distribution of the watermarked image. The entropy of the pixel value distribution is computed first. The Lorenz curve is used to measure the polarization degree of the pixel value distribution. In the pixel location distribution flow, the maximum entropy criteria is applied in segmenting the offset image into potentially tampered regions and unchanged regions. All-connected graph and 2-D Gaussian probability are utilized to obtain the probability distribution of the pixel location. Finally, the factitious tampering probability value of a pending detected image is computed through combining the weighting factors of pixel value and pixel location distribution. Experimental results show that the proposed method is more robust against the commonly used image processing operations, such as Gaussian noise, impulse noise, etc. Simultaneously, the proposed method achieves high sensitivity against factitious tampering. Full article

Multiscale entropy (MSE) is a widely used metric for characterizing the nonlinear dynamics of physiological processes. Significant variability, however, exists in the methodological approaches to MSE which may ultimately impact results and their interpretations. Using publications focused on balance-related center of pressure (COP) dynamics, we highlight sources of methodological heterogeneity that can impact study findings. Seventeen studies were systematically identified that employed MSE for characterizing COP displacement dynamics. We identified five key methodological procedures that varied significantly between studies: (1) data length; (2) frequencies of the COP dynamics analyzed; (3) sampling rate; (4) point matching tolerance and sequence length; and (5) filtering of displacement changes from drifts, fidgets, and shifts. We discuss strengths and limitations of the various approaches employed and supply flowcharts to assist in the decision making process regarding each of these procedures. Our guidelines are intended to more broadly inform the design and analysis of future studies employing MSE for continuous time series, such as COP. Full article

In this paper, the general wiretap channel with channel state information (CSI) at the transmitter and noiseless feedback is investigated, where the feedback is from the legitimate receiver to the transmitter, and the CSI is available at the transmitter in a causal or noncausal manner. The capacity-equivocation regions are determined for this model in both causal and noncausal cases, and the results are further explained via Gaussian and binary examples. For the Gaussian model, we find that in some particular cases, the noiseless feedback performs better than Chia and El Gamal’s CSI sharing scheme, i.e., the secrecy capacity of this feedback scheme is larger than that of the CSI sharing scheme. For the degraded binary model, we find that the noiseless feedback performs no better than Chia and El Gamal’s CSI sharing scheme. However, if the cross-over probability of the wiretap channel is large enough, we show that the two schemes perform the same. Full article

Based on phase space reconstruction and fractal dynamics in nonlinear dynamics, a method is proposed to extract and analyze the dynamics of the rotating stall in the impeller of centrifugal compressor, and some numerical examples are given to verify the results as well. First, the rotating stall of an existing low speed centrifugal compressor (LSCC) is numerically simulated, and the time series of pressure in the rotating stall is obtained at various locations near the impeller outlet. Then, the phase space reconstruction is applied to these pressure time series, and a low-dimensional dynamical system, which the dynamics properties are included in, is reconstructed. In phase space reconstruction, C–C method is used to obtain the key parameters, such as time delay and the embedding dimension of the reconstructed phase space. Further, the fractal characteristics of the rotating stall are analyzed in detail, and the fractal dimensions are given for some examples to measure the complexity of the flow in the post-rotating stall. The results show that the fractal structures could reveal the intrinsic dynamics of the rotating stall flow and could be considered as a characteristic to identify the rotating stall. Full article