Entropy Space Research Articles

Entropy paradigm in the theory of hierarchical active systems. Elements of conflict theory

Entropy paradigm in the theory of hierarchical active systems. Elements of conflict theory

Entropy and Loss: Paul Auster's In the Country of Last Things

Abstract This paper aims at understanding the postmodern victim's struggle for survival in a post-apocalyptic, unnamed metropolis depicted in Auster's novel In the Country of Last Things. It is a story about the loss of a known, recognizable world and the struggle to stay alive in a dystopian space. On the city streets, Auster's characters experience loneliness, disconnection and personal disintegration; individual memory is of no consequence in a place where everything is constantly shifting. With his depiction of a city in ruin, Auster offers a critique of Western civilization: this country of last things is what remains of an affluent society. The ruins, the inhumanity, the gradual disappearance of language all create a sterile urban landscape which is the result of hundreds of years of civilization. The lives of these urban individuals do not belong to them anymore, but to ‘the city being’ which has given up on its dwellers, on its history and on its language; everything is left to chance and the outcome can be surprising: the beginning of nothingness or of utopia. This article will explore issues such as the (post)apocalyptic paradigm, the entropy of space in an urban novel, the labyrinth as ‘central metaphor of postmodern fiction’ and the loss of identity through the loss of words.

Unification of Quantum and Gravity by Non Classical Information Entropy Space

A quantum entropy space is suggested as the fundamental arena describing the quantum effects. In the quantum regime the entropy is expressed as the superposition of many different Boltzmann entropies that span the space of the entropies before any measure. When a measure is performed the quantum entropy collapses to one component. A suggestive reading of the relational interpretation of quantum mechanics and of Bohm’s quantum potential in terms of the quantum entropy are provided. The space associated with the quantum entropy determines a distortion in the classical space of position, which appears as a Weyl-like gauge potential connected with Fisher information. This Weyl-like gauge potential produces a deformation of the moments which changes the classical action in such a way that Bohm’s quantum potential emerges as consequence of the non classical definition of entropy, in a non-Euclidean information space under the constraint of a minimum condition of Fisher information (Fisher Bohm- entropy). Finally, the possible quantum relativistic extensions of the theory and the connections with the problem of quantum gravity are investigated. The non classical thermodynamic approach to quantum phenomena changes the geometry of the particle phase space. In the light of the representation of gravity in ordinary phase space by torsion in the flat space (Teleparallel gravity), the change of geometry in the phase space introduces quantum phenomena in a natural way. This gives a new force to F. Shojai’s and A. Shojai’s theory where the geometry of space-time is highly coupled with a quantum potential whose origin is not the Schrödinger equation but the non classical entropy of a system of many particles that together change the geometry of the phase space of the positions (entanglement). In this way the non classical thermodynamic changes the classical geodetic as a consequence of the quantum phenomena and quantum and gravity are unified. Quantum affects geometry of multidimensional phase space and gravity changes in any point the torsion in the ordinary four-dimensional Lorenz space-time metric.

Analysis of Vibration Signals of Scroll Compressor Based on Information Entropy

In order to make a quantitative description for the running status of the scroll compressor, a fault diagnosis method of information entropy is proposed on the basis of the theory of entropy. This method is based on singular spectrum entropy in time domain, power spectrum entropy in frequency domain, wavelet power spectrum entropy and wavelet space feature spectrum entropy in time-frequency domain, which is used as the comprehensive appraisal index of quantitative feature for vibration status of scroll compressor. Under condition of invariable speed operation, the identification of natural frequency of is carried out. Meanwhile, the influence of the axial vibration of moving scroll, radial compliance mechanism and slight liquid slugging on the scroll compressor is analyzed quantitatively. Three forms of periodic cataclysm of moving scroll under variable speed operation and the variation of information entropy with rotational speed are disclosed.

De Sitter entropy from a lower dimensional black hole

An alternative method compute the entropy of de Sitter spacetime for dimensions higher than or equal to five is presented. It is shown that de Sitter entropy may be obtained from the Bekenstein--Hawking entropy of a lower-dimensional black hole. This result follows from the existence of a one-to-one correspondence between de Sitter and a spacetime containing a black hole localized on a $p$-brane. Under this correspondence and due to the holographic principle, the entropy of a five-dimensional de Sitter space may be obtained from that of a BTZ black hole localized on a 2-brane. For dimensions higher than five, de Sitter entropy is identified with the entropy of a Schwarzschild--de Sitter black hole localized on a ($d\ensuremath{-}3$)-brane.

The volume entropy of local Hermitian symmetric space of noncompact type

We calculate the volume entropy of local Hermitian symmetric spaces of noncompact type in terms of its invariant r, a, b.

Area spectra of extreme Kerr and nearly extreme Kerr–Newmann black holes from quasinormal modes

The area spectra of extreme Kerr and nearly extreme Kerr–Newmann black holes are investigated from quasinormal modes via Maggiore’s physical interpretation of quasinormal modes. Using the first law of black hole thermodynamics and the action variable quantization, we arrive at consistent equally spaced area and entropy spectra. Results show that the spectra are irrelevant to the parameters of the black holes and the perturbation fields, which fully agree with Bekensteins original conjecture. In the calculations, we have defined the corresponding Hawking temperatures of the black holes following the suggestion of Makela et al. to avoid the zero temperature and to guarantee the (nearly-) extreme black holes quantizable.

Spectral triples for hyperbolic dynamical systems

Spectral triples are defined for C*-algebras associated with hyperbolic dynamical systems known as Smale spaces. The spectral dimension of one of these spectral triples is shown to recover the topological entropy of the Smale space.

Thermodynamics of conformal fields in topologically non-trivial space-time backgrounds

We analyze the finite temperature behaviour of massless conformally coupled scalar fields in homogeneous lens spaces $S^3/{\mathbb Z}_p$. High and low temperature expansions are explicitly computed and the behavior of thermodynamic quantities under thermal duality is scrutinized. The analysis of the entropy of the different lens spaces in the high-temperature limit points out the appearance of a topological nonextensive entropy, besides the standard Stefan-Boltzmann extensive term. The remaining terms are exponentially suppressed by the temperature. The topological entropy appears as a subleading correction to the free energy that can be obtained from the determinant of the lens space conformal Laplacian operator. In the low-temperature limit the leading term in the free energy is the Casimir energy and there is no trace of any power correction in any lens space. In fact, the remaining corrections are always exponentially suppressed by the inverse of the temperature. The duality between the results of both expansions is further analyzed in the paper.

QUANTIZATION OF ENTROPY SPECTRA OF BLACK HOLES

From the quasinormal modes (QNM) of black holes, we obtain the quantizations of the entropy and horizon area of black holes via Bohr–Sommerfeld quantization, based on Bohr's correspondence principle. For this, we identify the appropriate action variable of the classical system corresponding to a black hole. By considering the BTZ black holes in topologically massive gravity as well as Einstein gravity, it is found that the spectra of not the horizon areas but the entropies of black holes are equally spaced. We also propose that other characteristic modes of black holes, which are non-QNM or holographic QNM, can be used in quantization of entropy spectra just like QNM. From these modes, it is found that only the entropy spectrum of the warped AdS3 black hole is equally spaced as well. Furthermore, by considering a scattering problem in a black hole, we propose that the total transmission modes and total reflection modes of black holes can be regarded as characteristic modes of black holes and result in the equally spaced entropy of the Kerr and Reissner–Nordström black holes. Finally, we conclude that there is a universal behavior that the entropy spectra of various black holes are equally spaced.

Some properties of positive entropy maps

AbstractWe prove that the stable classes for continuous maps on compact metric spaces have measure zero with respect to any ergodic invariant measure with positive entropy. Then, every continuous map with positive topological entropy on a compact metric space has uncountably many stable classes. We also prove that every continuous map with positive topological entropy of a compact metric space cannot be Lyapunov stable on its recurrent set. For homeomorphisms on compact metric spaces we prove that the sets of heteroclinic points, and sinks in the canonical coordinates case, have zero measure with respect to any ergodic invariant measure with positive entropy. These results generalize those of Fedorenko and Smital [Maps of the interval Ljapunov stable on the set of nonwandering points. Acta Math. Univ. Comenian. (N.S.)60 (1) (1991), 11–14], Huang and Ye [Devaney’s chaos or 2-scattering implies Li–Yorke’s chaos. Topology Appl.117 (3) (2002), 259–272], Reddy [The existence of expansive homeomorphisms on manifolds. Duke Math. J.32 (1965), 627–632], Reddy and Robertson [Sources, sinks and saddles for expansive homeomorphisms with canonical coordinates. Rocky Mountain J. Math.17 (4) (1987), 673–681], Sindelarova [A counterexample to a statement concerning Lyapunov stability. Acta Math. Univ. Comenian. 70 (2001), 265–268], and Zhou [Some equivalent conditions for self-mappings of a circle. Chinese Ann. Math. Ser. A12(suppl.) (1991), 22–27].

Quantization of the Kerr-Sen Black Hole Entropy via Adiabatic Invariance

Imposing the Bohr-Sommerfeld quantization rule to the adiabatic invariant quantity, we study the quantum spectrum of entropy for the Kerr-Sen black hole. The equally spaced entropy spectrum is derived. However, whether the spacing of the area spectrum is equidistant spaced or not, is still somewhat controversial.

Particle Filter Algorithm for Object Tracking Based on Color Local Entropy

To achieve accurate visual object tracking and overcome the difficulties brought by the object deformation, occlusion, and illumination variations, a particle filter for object tracking algorithm based on color local entropy (CLE) is proposed. First we improved the traditional histogram weighted function by using a scale factor. Then, for the shortcoming that the color feature is sensitive to illumination and environmental interference, a color local entropy object observation model is constructed by mapping the object from color feature space to local entropy space. In addition, an adaptive updating strategy of the object template is designed and the number of particle is adjusted dynamically according to the tracking performance. The experimental results show that compared with several existing algorithms, the proposed algorithm is more effective and robust for the real-time object tracking under the situation of illumination variation, object occlusion, and nonlinear motion.

Entropy and Flow-based Approach for Anomalous Traffic Filtering

Research Tools in Anomaly-based Intrusion Detection are highly dependent on appropriate traffic trace data. Traditional datasets present several issues such as: removal of sensitive information (anonymization) and insufficient number or volume of attack instances, which limit their quality for the design and evaluation of A-NIDSs. In this paper, we present a method for anomalous traffic filtering which can be used for generating anomaly-free traffic traces. The sanitized dataset can be used to improve the computation of the behaviour profiles during the training stage. The proposal is based on the construction and statistical analysis of the flow-level entropy space for the identification of outliers using three entropy estimators. Empirical results showed that the new traffic traces of the sanitized dataset have a distributional similarity among them greater than that presented among the original datasets.

Information theory in nonlinear error growth dynamics and its application to predictability: Taking the Lorenz system as an example

In nonlinear error growth dynamics, the initial error cannot be accurately determined, and the forecast error, which is also uncertain, can be considered to be a random variable. Entropy in information theory is a natural measure of the uncertainty of a random variable associated with a probability distribution. This paper effectively combines statistical information theory and nonlinear error growth dynamics, and introduces some fundamental concepts of entropy in information theory for nonlinear error growth dynamics. Entropy based on nonlinear error can be divided into time entropy and space entropy, which are used to estimate the predictabilities of the whole dynamical system and each of its variables. This is not only applicable for investigating the dependence between any two variables of a multivariable system, but also for measuring the influence of each variable on the predictability of the whole system. Taking the Lorenz system as an example, the entropy of nonlinear error is applied to estimate predictability. The time and space entropies are used to investigate the spatial distribution of predictability of the whole Lorenz system. The results show that when moving around two chaotic attractors or near the edge of system space, a Lorenz system with lower sensitivity to the initial field behaves with higher predictability and a longer predictability limit. The example analysis of predictability of the Lorenz system demonstrates that the predictability estimated by the entropy of nonlinear error is feasible and effective, especially for estimation of predictability of the whole system. This provides a theoretical foundation for further work in estimating real atmospheric multivariable joint predictability.

Fabric Defect Detection Based on Local Entropy

To solve the problem of automated defect detection for textile fabrics, this paper proposed a method for fabric defect detection which is based on local entropy. The method can transform the original gray image space for the entropy space and enhance the different organization structure which is conducive to extract the damage texture region. In the experiment, divided the fabric image to the same size local window, and chosen the smallest value of local entropy window region to segment the defects. The experimental result shown that this method can avoid the whole image complex operations and possess high recognition accuracy.

SPECTROSCOPY OF ROTATING BLACK HOLES VIA AN ACTION INVARIANCE

The spectroscopy of rotating black holes are investigated via an action invariance of black holes. Without using the quasinormal modes of black holes, the area and entropy spectrum for Kerr and Kerr–Newman black holes are calculated, respectively. For these rotating black holes, the same result of the equally spaced area and entropy spectrum is derived by utilizing the action invariance and with the help of Bohr–Sommerfield quantization rule. The present black hole spectroscopy is consistent not only to the result of other researches by the action invariance but also the original Bekenstein's spectra.

An intertwining chaotic maps based image encryption scheme

In this paper, a new image encryption scheme is proposed that uses intertwining chaotic maps to enhance security and key length. In the substitution process, six randomly chosen odd integers are used to permute and then XORed with the first chaotic key to shuffle and alter the image pixels. Byte substitution has also been applied and the resultant values are XORed with the second chaotic key to improve the security against the known/chosen-plain text attack and to increase nonlinearity. In the diffusion process, the pixel values are altered sequentially with various operations which include nonlinear diffusion using the first chaotic key, subdiagonal diffusion of adjacent pixels and XORing with the third chaotic key. The security and performance of the proposed image encryption technique have been analyzed using statistical analysis, sensitivity analysis, key space analysis, differential analysis, and entropy analysis. The simulation shows that a single bit of key or pixel difference of the plain-image will change almost all the pixels in the cipher-image (\(\mathrm{NPCR}>99.63\) %), and the unified average changing intensity is high (\(\mathrm{UACI}>33.43\) %). Since the entropy is found to be close to the theoretical value, we observed that the information leakage is negligible, and hence the scheme is highly secure. The experimental results show that the performance of the proposed scheme is secure and fast.

Boundary distortion rate in synchronized systems: Geometrical meaning of entropy

The geometrical meaning of the Kolmogorov entropy is studied. The relation between the entropy and boundary distortion rate in the phase space is obtained for a wide class of symbolic dynamical systems, namely synchronized systems.

Entropy Conservation in the Transition of Schwarzschild-de Sitter Space to de Sitter Space through Tunneling

We revisit Parikh—Wilczek tunneling through the de Sitter horizon and obtain the tunneling rate in Schwarzschild-de Sitter space, which is non-thermal and closely related to the change of entropy. We discuss the thermodynamics of Schwarzschild-de Sitter space and show existence of correlation which can ensure conservation of the total entropy in the transition process of Schwarzschild-de Sitter space to de Sitter space. The correlation and the conserved entropy provide a way to explain the entropy in empty de Sitter space.