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Entropy, Volume 15, Issue 8 (August 2013), Pages 2874-3311

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Research

Jump to: Review

Open AccessArticle Time Evolution of Relative Entropies for Anomalous Diffusion
Entropy 2013, 15(8), 2989-3006; doi:10.3390/e15082989
Received: 26 June 2013 / Revised: 17 July 2013 / Accepted: 18 July 2013 / Published: 26 July 2013
Cited by 8 | PDF Full-text (298 KB) | HTML Full-text | XML Full-text
Abstract
The entropy production paradox for anomalous diffusion processes describes a phenomenon where one-parameter families of dynamical equations, falling between the diffusion and wave equations, have entropy production rates (Shannon, Tsallis or Renyi) that increase toward the wave equation limit unexpectedly. Moreover, also surprisingly,
[...] Read more.
The entropy production paradox for anomalous diffusion processes describes a phenomenon where one-parameter families of dynamical equations, falling between the diffusion and wave equations, have entropy production rates (Shannon, Tsallis or Renyi) that increase toward the wave equation limit unexpectedly. Moreover, also surprisingly, the entropy does not order the bridging regime between diffusion and waves at all. However, it has been found that relative entropies, with an appropriately chosen reference distribution, do. Relative entropies, thus, provide a physically sensible way of setting which process is “nearer” to pure diffusion than another, placing pure wave propagation, desirably, “furthest” from pure diffusion. We examine here the time behavior of the relative entropies under the evolution dynamics of the underlying one-parameter family of dynamical equations based on space-fractional derivatives. Full article
(This article belongs to the Special Issue Distance in Information and Statistical Physics Volume 2)
Open AccessArticle Optimization of Curvilinear Tracing Applied to Solar Physics and Biophysics
Entropy 2013, 15(8), 3007-3030; doi:10.3390/e15083007
Received: 23 May 2013 / Revised: 4 July 2013 / Accepted: 18 July 2013 / Published: 26 July 2013
Cited by 9 | PDF Full-text (11053 KB) | HTML Full-text | XML Full-text
Abstract
We developed an automated pattern recognition code that is particularly well suited to extract one-dimensional curvilinear features from two-dimensional digital images. A former version of this Oriented Coronal Curved Loop Tracing (OCCULT) code was applied to spacecraft images of magnetic loops in the
[...] Read more.
We developed an automated pattern recognition code that is particularly well suited to extract one-dimensional curvilinear features from two-dimensional digital images. A former version of this Oriented Coronal Curved Loop Tracing (OCCULT) code was applied to spacecraft images of magnetic loops in the solar corona, recorded with the NASA spacecraft, Transition Region And Coronal Explorer (TRACE), in extreme ultra-violet wavelengths. Here, we apply an advanced version of this code (OCCULT-2), also, to similar images from the Solar Dynamics Observatory (SDO), to chromospheric H-α images obtained with the Swedish Solar Telescope (SST) and to microscopy images of microtubule filaments in live cells in biophysics. We provide a full analytical description of the code, optimize the control parameters and compare the automated tracing with visual/manual methods. The traced structures differ by up to 16 orders of magnitude in size, which demonstrates the universality of the tracing algorithm. Full article
(This article belongs to the Special Issue Advanced Signal Processing in Heliospheric Physics)
Open AccessArticle What Do Leaders Know?
Entropy 2013, 15(8), 3031-3044; doi:10.3390/e15083031
Received: 18 June 2013 / Revised: 19 July 2013 / Accepted: 22 July 2013 / Published: 26 July 2013
Cited by 1 | PDF Full-text (340 KB) | HTML Full-text | XML Full-text
Abstract
The ability of a society to make the right decisions on relevant matters relies on its capability to properly aggregate the noisy information spread across the individuals of which it is made. In this paper, we study the information aggregation performance of a
[...] Read more.
The ability of a society to make the right decisions on relevant matters relies on its capability to properly aggregate the noisy information spread across the individuals of which it is made. In this paper, we study the information aggregation performance of a stylized model of a society, whose most influential individuals—the leaders—are highly connected among themselves and uninformed. Agents update their state of knowledge in a Bayesian manner by listening to their neighbors. We find analytical and numerical evidence of a transition, as a function of the noise level in the information initially available to agents, from a regime where information is correctly aggregated, to one where the population reaches consensus on the wrong outcome with finite probability. Furthermore, information aggregation depends in a non-trivial manner on the relative size of the clique of leaders, with the limit of a vanishingly small clique being singular. Full article
(This article belongs to the Special Issue Social Networks and Information Diffusion)
Open AccessArticle Casimir Friction between Dense Polarizable Media
Entropy 2013, 15(8), 3045-3064; doi:10.3390/e15083045
Received: 28 June 2013 / Revised: 17 July 2013 / Accepted: 22 July 2013 / Published: 29 July 2013
Cited by 11 | PDF Full-text (263 KB) | HTML Full-text | XML Full-text
Abstract
The present paper—a continuation of our recent series of papers on Casimir friction for a pair of particles at low relative particle velocity—extends the analysis, so as to include dense media. The situation becomes, in this case, more complex, due to induced dipolar
[...] Read more.
The present paper—a continuation of our recent series of papers on Casimir friction for a pair of particles at low relative particle velocity—extends the analysis, so as to include dense media. The situation becomes, in this case, more complex, due to induced dipolar correlations, both within planes and between planes. We show that the structure of the problem can be simplified by regarding the two half-planes as a generalized version of a pair of particles. It turns out that macroscopic parameters, such as permittivity, suffice to describe the friction, also in the finite density case. The expression for the friction force per unit surface area becomes mathematically well-defined and finite at finite temperature. We give numerical estimates and compare them with those obtained earlier by Pendry (1997) and by Volokitin and Persson (2007). We also show in an appendix how the statistical methods that we are using correspond to the field theoretical methods more commonly in use. Full article
Open AccessArticle Flow of Information during an Evolutionary Process: The Case of Influenza A Viruses
Entropy 2013, 15(8), 3065-3087; doi:10.3390/e15083065
Received: 14 March 2013 / Revised: 18 July 2013 / Accepted: 23 July 2013 / Published: 29 July 2013
Cited by 1 | PDF Full-text (713 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
The hypothesis that Mutual Information (MI) dendrograms of influenza A viruses reflect informational groups generated during viral evolutionary processes is put forward. Phylogenetic reconstructions are used for guidance and validation of MI dendrograms. It is found that MI profiles display an oscillatory behavior
[...] Read more.
The hypothesis that Mutual Information (MI) dendrograms of influenza A viruses reflect informational groups generated during viral evolutionary processes is put forward. Phylogenetic reconstructions are used for guidance and validation of MI dendrograms. It is found that MI profiles display an oscillatory behavior for each of the eight RNA segments of influenza A. It is shown that dendrograms of MI values of geographically and historically different segments coming from strains of RNA virus influenza A turned out to be unexpectedly similar to the clusters, but not with the topology of the phylogenetic trees. No matter how diverse the RNA sequences are, MI dendrograms crisply discern actual viral subtypes together with gain and/or losses of information that occur during viral evolution. The amount of information during a century of evolution of RNA segments of influenza A is measured in terms of bits of information for both human and avian strains. Overall the amount of information of segments of pandemic strains oscillates during viral evolution. To our knowledge this is the first description of clades of information of the viral subtypes and the estimation of the flow content of information, measured in bits, during an evolutionary process of a virus. Full article
Open AccessArticle Folding Kinetics of Riboswitch Transcriptional Terminators and Sequesterers
Entropy 2013, 15(8), 3088-3099; doi:10.3390/e15083088
Received: 13 June 2013 / Revised: 15 July 2013 / Accepted: 22 July 2013 / Published: 31 July 2013
Cited by 3 | PDF Full-text (180 KB) | HTML Full-text | XML Full-text
Abstract
To function as gene regulatory elements in response to environmental signals, riboswitches must adopt specific secondary structures on appropriate time scales. We employ kinetic Monte Carlo simulation to model the time-dependent folding during transcription of thiamine pyrophosphate (TPP) riboswitch expression platforms. According to
[...] Read more.
To function as gene regulatory elements in response to environmental signals, riboswitches must adopt specific secondary structures on appropriate time scales. We employ kinetic Monte Carlo simulation to model the time-dependent folding during transcription of thiamine pyrophosphate (TPP) riboswitch expression platforms. According to our simulations, riboswitch transcriptional terminators, which must adopt a specific hairpin configuration by the time they have been transcribed, fold with higher efficiency than Shine-Dalgarno sequesterers, whose proper structure is required only at the time of ribosomal binding. Our findings suggest both that riboswitch transcriptional terminator sequences have been naturally selected for high folding efficiency, and that sequesterers can maintain their function even in the presence of significant misfolding. Full article
(This article belongs to the Special Issue Entropy and RNA Structure, Folding and Mechanics)
Open AccessArticle On the Topological Entropy of Some Skew-Product Maps
Entropy 2013, 15(8), 3100-3108; doi:10.3390/e15083100
Received: 5 July 2013 / Revised: 25 July 2013 / Accepted: 26 July 2013 / Published: 31 July 2013
Cited by 1 | PDF Full-text (294 KB) | HTML Full-text | XML Full-text
Abstract
The aim of this short note is to compute the topological entropy for a family of skew-product maps, whose base is a subshift of finite type, and the fiber maps are homeomorphisms defined in one dimensional spaces. We show that the skew-product map
[...] Read more.
The aim of this short note is to compute the topological entropy for a family of skew-product maps, whose base is a subshift of finite type, and the fiber maps are homeomorphisms defined in one dimensional spaces. We show that the skew-product map does not increase the topological entropy of the subshift. Full article
(This article belongs to the Special Issue Dynamical Systems) Print Edition available
Open AccessArticle Estimation Bias in Maximum Entropy Models
Entropy 2013, 15(8), 3109-3129; doi:10.3390/e15083109
Received: 25 June 2013 / Revised: 25 July 2013 / Accepted: 29 July 2013 / Published: 2 August 2013
PDF Full-text (3902 KB) | HTML Full-text | XML Full-text
Abstract
Maximum entropy models have become popular statistical models in neuroscience and other areas in biology and can be useful tools for obtaining estimates of mutual information in biological systems. However, maximum entropy models fit to small data sets can be subject to sampling
[...] Read more.
Maximum entropy models have become popular statistical models in neuroscience and other areas in biology and can be useful tools for obtaining estimates of mutual information in biological systems. However, maximum entropy models fit to small data sets can be subject to sampling bias; i.e., the true entropy of the data can be severely underestimated. Here, we study the sampling properties of estimates of the entropy obtained from maximum entropy models. We focus on pairwise binary models, which are used extensively to model neural population activity. We show that if the data is well described by a pairwise model, the bias is equal to the number of parameters divided by twice the number of observations. If, however, the higher order correlations in the data deviate from those predicted by the model, the bias can be larger. Using a phenomenological model of neural population recordings, we find that this additional bias is highest for small firing probabilities, strong correlations and large population sizes—for the parameters we tested, a factor of about four higher. We derive guidelines for how long a neurophysiological experiment needs to be in order to ensure that the bias is less than a specified criterion. Finally, we show how a modified plug-in estimate of the entropy can be used for bias correction. Full article
(This article belongs to the Special Issue Estimating Information-Theoretic Quantities from Data)
Open AccessArticle Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information?
Entropy 2013, 15(8), 3130-3147; doi:10.3390/e15083220
Received: 21 June 2013 / Revised: 24 July 2013 / Accepted: 24 July 2013 / Published: 2 August 2013
Cited by 2 | PDF Full-text (440 KB)
Abstract
A quantum measurement can be regarded as a communication channel, in which the parameters of the state are expressed only in the probabilities of the outcomes of the measurement. We begin this paper by considering, in a non-quantum-mechanical setting, the problem of communicating
[...] Read more.
A quantum measurement can be regarded as a communication channel, in which the parameters of the state are expressed only in the probabilities of the outcomes of the measurement. We begin this paper by considering, in a non-quantum-mechanical setting, the problem of communicating through probabilities. For example, a sender, Alice, wants to convey to a receiver, Bob, the value of a continuous variable, θ, but her only means of conveying this value is by sending Bob a coin in which the value of θ is encoded in the probability of heads. We ask what the optimal encoding is when Bob will be allowed to flip the coin only a finite number of times. As the number of tosses goes to infinity, we find that the optimal encoding is the same as what nature would do if we lived in a world governed by real-vector-space quantum theory. We then ask whether the problem might be modified, so that the optimal communication strategy would be consistent with standard, complex-vector-space quantum theory. Full article
(This article belongs to the Special Issue Quantum Information 2012)
Open AccessArticle Low-Temperature Behaviour of Social and Economic Networks
Entropy 2013, 15(8), 3148-3169; doi:10.3390/e15083238
Received: 19 June 2013 / Revised: 17 July 2013 / Accepted: 30 July 2013 / Published: 5 August 2013
Cited by 3 | PDF Full-text (472 KB)
Abstract
Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely interconnected nodes. Several models, including ensembles of networks, also known
[...] Read more.
Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely interconnected nodes. Several models, including ensembles of networks, also known in social science as Exponential Random Graphs, have been proposed with the aim of reproducing each of these properties in isolation. Here, we define a generalized ensemble of graphs by introducing the concept of graph temperature, controlling the degree of topological optimization of a network. We consider the temperature-dependent version of both existing and novel models and show that all the aforementioned topological properties can be simultaneously understood as the natural outcomes of an optimized, low-temperature topology. We also show that seemingly different graph models, as well as techniques used to extract information from real networks are all found to be particular low-temperature cases of the same generalized formalism. One such technique allows us to extend our approach to real weighted networks. Our results suggest that a low graph temperature might be a ubiquitous property of real socio-economic networks, placing conditions on the diffusion of information across these systems. Full article
(This article belongs to the Special Issue Social Networks and Information Diffusion)
Open AccessArticle A Maximum Entropy-Based Chaotic Time-Variant Fragile Watermarking Scheme for Image Tampering Detection
Entropy 2013, 15(8), 3170-3185; doi:10.3390/e15083260
Received: 16 April 2013 / Revised: 27 July 2013 / Accepted: 29 July 2013 / Published: 5 August 2013
Cited by 8 | PDF Full-text (1932 KB)
Abstract
The fragile watermarking technique is used to protect intellectual property rights while also providing security and rigorous protection. In order to protect the copyright of the creators, it can be implanted in some representative text or totem. Because all of the media on
[...] Read more.
The fragile watermarking technique is used to protect intellectual property rights while also providing security and rigorous protection. In order to protect the copyright of the creators, it can be implanted in some representative text or totem. Because all of the media on the Internet are digital, protection has become a critical issue, and determining how to use digital watermarks to protect digital media is thus the topic of our research. This paper uses the Logistic map with parameter u = 4 to generate chaotic dynamic behavior with the maximum entropy 1. This approach increases the security and rigor of the protection. The main research target of information hiding is determining how to hide confidential data so that the naked eye cannot see the difference. Next, we introduce one method of information hiding. Generally speaking, if the image only goes through Arnold’s cat map and the Logistic map, it seems to lack sufficient security. Therefore, our emphasis is on controlling Arnold’s cat map and the initial value of the chaos system to undergo small changes and generate different chaos sequences. Thus, the current time is used to not only make encryption more stringent but also to enhance the security of the digital media. Full article
(This article belongs to the Special Issue Dynamical Systems) Print Edition available
Open AccessArticle Linearized Transfer Entropy for Continuous Second Order Systems
Entropy 2013, 15(8), 3186-3204; doi:10.3390/e15083276
Received: 22 May 2013 / Revised: 5 July 2013 / Accepted: 18 July 2013 / Published: 7 August 2013
Cited by 4 | PDF Full-text (397 KB)
Abstract
The transfer entropy has proven a useful measure of coupling among components of a dynamical system. This measure effectively captures the influence of one system component on the transition probabilities (dynamics) of another. The original motivation for the measure was to quantify such
[...] Read more.
The transfer entropy has proven a useful measure of coupling among components of a dynamical system. This measure effectively captures the influence of one system component on the transition probabilities (dynamics) of another. The original motivation for the measure was to quantify such relationships among signals collected from a nonlinear system. However, we have found the transfer entropy to also be a useful concept in describing linear coupling among system components. In this work we derive the analytical transfer entropy for the response of coupled, second order linear systems driven with a Gaussian random process. The resulting expression is a function of the auto- and cross-correlation functions associated with the system response for different degrees-of-freedom. We show clearly that the interpretation of the transfer entropy as a measure of "information flow" is not always valid. In fact, in certain instances the "flow" can appear to switch directions simply by altering the degree of linear coupling. A safer way to view the transfer entropy is as a measure of the ability of a given system component to predict the dynamics of another. Full article
(This article belongs to the Special Issue Transfer Entropy)
Open AccessArticle Local Feature Extraction and Information Bottleneck-Based Segmentation of Brain Magnetic Resonance (MR) Images
Entropy 2013, 15(8), 3205-3218; doi:10.3390/e15083295
Received: 23 May 2013 / Revised: 24 July 2013 / Accepted: 25 July 2013 / Published: 9 August 2013
Cited by 2 | PDF Full-text (1462 KB)
Abstract
Automated tissue segmentation of brain magnetic resonance (MR) images has attracted extensive research attention. Many segmentation algorithms have been proposed for this issue. However, due to the existence of noise and intensity inhomogeneity in brain MR images, the accuracy of the segmentation results
[...] Read more.
Automated tissue segmentation of brain magnetic resonance (MR) images has attracted extensive research attention. Many segmentation algorithms have been proposed for this issue. However, due to the existence of noise and intensity inhomogeneity in brain MR images, the accuracy of the segmentation results is usually unsatisfactory. In this paper, a high-accuracy brain MR image segmentation algorithm based on the information bottleneck (IB) method is presented. In this approach, the MR image is first mapped into a “local-feature space”, then the IB method segments the brain MR image through an information theoretic formulation in this local-feature space. It automatically segments the image into several clusters of voxels, by taking the intensity information and spatial information of voxels into account. Then, after the IB-based clustering, each cluster of voxels is classified into one type of brain tissue by threshold methods. The performance of the algorithm is studied based on both simulated and real T1-weighted 3D brain MR images. Our results show that, compared with other well-known brain image segmentation algorithms, the proposed algorithm can improve the accuracy of the segmentation results substantially. Full article
Open AccessArticle Limits and Optimization of Power Input or Output of Actual Thermal Cycles
Entropy 2013, 15(8), 3219-3248; doi:10.3390/e15083309
Received: 24 April 2013 / Revised: 24 June 2013 / Accepted: 6 August 2013 / Published: 12 August 2013
Cited by 20 | PDF Full-text (280 KB)
Abstract
In classical thermodynamic, maximum power obtained from system (or minimum power supplied to system) defined as availability (exergy), but availability term is only used for reversible systems. In reality, there is no reversible system, all systems are irreversible, because reversible cycles doesn’t include
[...] Read more.
In classical thermodynamic, maximum power obtained from system (or minimum power supplied to system) defined as availability (exergy), but availability term is only used for reversible systems. In reality, there is no reversible system, all systems are irreversible, because reversible cycles doesn’t include constrains like time or size and they operates in quasi-equilibrium state. Purpose of this study is to define limits of the all basic thermodynamic cycles and to provide finite-time exergy models for irreversible cycles and to obtain the maximum (or minimum) available power for irreversible (finite-time exergy) cycles. In this study, available power optimization and performance limits were defined all basic irreversible thermodynamic cycles, by using first and second law of thermodynamic. Finally, these results were evaluated in terms of cycles’ first and second law efficiency, COP, power output (or input) and exergy destruction. Full article
Open AccessArticle Truncation Effects of Shift Function Methods in Bulk Water Systems
Entropy 2013, 15(8), 3249-3264; doi:10.3390/e15083339
Received: 30 June 2013 / Revised: 5 August 2013 / Accepted: 7 August 2013 / Published: 13 August 2013
Cited by 8 | PDF Full-text (240 KB)
Abstract
A reduction of the cost for long-range interaction calculation is essential for large-scale molecular systems that contain a lot of point charges. Cutoff methods are often used to reduce the cost of long-range interaction calculations. Molecular dynamics (MD) simulations can be accelerated by
[...] Read more.
A reduction of the cost for long-range interaction calculation is essential for large-scale molecular systems that contain a lot of point charges. Cutoff methods are often used to reduce the cost of long-range interaction calculations. Molecular dynamics (MD) simulations can be accelerated by using cutoff methods; however, simple truncation or approximation of long-range interactions often offers serious defects for various systems. For example, thermodynamical properties of polar molecular systems are strongly affected by the treatment of the Coulombic interactions and may lead to unphysical results. To assess the truncation effect of some cutoff methods that are categorized as the shift function method, MD simulations for bulk water systems were performed. The results reflect two main factors, i.e., the treatment of cutoff boundary conditions and the presence/absence of the theoretical background for the long-range approximation. Full article
(This article belongs to the Special Issue Molecular Dynamics Simulation) Print Edition available
Open AccessArticle Synchronization of a Class of Fractional-Order Chaotic Neural Networks
Entropy 2013, 15(8), 3265-3276; doi:10.3390/e15083355
Received: 5 June 2013 / Revised: 3 August 2013 / Accepted: 5 August 2013 / Published: 14 August 2013
Cited by 31 | PDF Full-text (421 KB)
Abstract
The synchronization problem is studied in this paper for a class of fractional-order chaotic neural networks. By using the Mittag-Leffler function, M-matrix and linear feedback control, a sufficient condition is developed ensuring the synchronization of such neural models with the Caputo fractional derivatives.
[...] Read more.
The synchronization problem is studied in this paper for a class of fractional-order chaotic neural networks. By using the Mittag-Leffler function, M-matrix and linear feedback control, a sufficient condition is developed ensuring the synchronization of such neural models with the Caputo fractional derivatives. The synchronization condition is easy to verify, implement and only relies on system structure. Furthermore, the theoretical results are applied to a typical fractional-order chaotic Hopfield neural network, and numerical simulation demonstrates the effectiveness and feasibility of the proposed method. Full article
(This article belongs to the Special Issue Dynamical Systems) Print Edition available
Open AccessArticle Fluctuations in the Energetic Properties of a Spark-Ignition Engine Model with Variability
Entropy 2013, 15(8), 3277-3296; doi:10.3390/e15083367
Received: 8 June 2013 / Revised: 30 July 2013 / Accepted: 13 August 2013 / Published: 19 August 2013
Cited by 5 | PDF Full-text (11348 KB)
Abstract
We study the energetic functions obtained in a simulated spark-ignited engine that incorporates cyclic variability through a quasi-dimensional combustion model. Our analyses are focused on the effects of the fuel-air equivalence ratio of the mixture simultaneously over the cycle-to-cycle fluctuations of heat release
[...] Read more.
We study the energetic functions obtained in a simulated spark-ignited engine that incorporates cyclic variability through a quasi-dimensional combustion model. Our analyses are focused on the effects of the fuel-air equivalence ratio of the mixture simultaneously over the cycle-to-cycle fluctuations of heat release (QR) and the performance outputs, such as the power (P) and the efficiency (QR). We explore the fluctuant behavior for QR, P and n related to random variations of the basic physical parameters in an entrainment or eddy-burning combustion model. P and n show triangle shaped first return maps, while QR exhibits a structured map, especially at intermediated fuel-air ratios. Structure disappears to a considerable extent in the case of heat release and close-to-stoichiometry fuel-air ratios. By analyzing the fractal dimension to explore the presence of correlations at different scales, we find that whereas QR displays short-range correlations for intermediate values of the fuel ratio, both P and n are characterized by a single scaling exponent, denoting irregular fluctuations. A novel noisy loop-shaped P vs. n plot for a large number of engine cycles is obtained. This plot, which evidences different levels of irreversibilities as the fuel ratio changes, becomes the observed loop P vs. n curve when fluctuations are disregarded, and thus, only the mean values for efficiency and power are considered. Full article
Open AccessArticle Entropy and Computation: The Landauer-Bennett Thesis Reexamined
Entropy 2013, 15(8), 3297-3311; doi:10.3390/e15083297
Received: 1 July 2013 / Revised: 2 August 2013 / Accepted: 14 August 2013 / Published: 21 August 2013
Cited by 2 | PDF Full-text (274 KB) | HTML Full-text | XML Full-text
Abstract
The so-called Landauer-Bennett thesis says that logically irreversible operations (physically implemented) such as erasure necessarily involve dissipation by at least kln2 per bit of lost information. We identify the physical conditions that are necessary and sufficient for erasure and show that the
[...] Read more.
The so-called Landauer-Bennett thesis says that logically irreversible operations (physically implemented) such as erasure necessarily involve dissipation by at least kln2 per bit of lost information. We identify the physical conditions that are necessary and sufficient for erasure and show that the thesis does not follow from the principles of classical mechanics. In particular, we show that even if one assumes that information processing is constrained by the laws of classical mechanics, it need not be constrained by the Second Law of thermodynamics. Full article
(This article belongs to the Special Issue Maxwell’s Demon 2013)

Review

Jump to: Research

Open AccessReview Towards Realising Secure and Efficient Image and Video Processing Applications on Quantum Computers
Entropy 2013, 15(8), 2874-2974; doi:10.3390/e15082874
Received: 15 April 2013 / Revised: 5 July 2013 / Accepted: 11 July 2013 / Published: 26 July 2013
Cited by 11 | PDF Full-text (3725 KB) | HTML Full-text | XML Full-text
Abstract
Exploiting the promise of security and efficiency that quantum computing offers, the basic foundations leading to commercial applications for quantum image processing are proposed. Two mathematical frameworks and algorithms to accomplish the watermarking of quantum images, authentication of ownership of already watermarked images
[...] Read more.
Exploiting the promise of security and efficiency that quantum computing offers, the basic foundations leading to commercial applications for quantum image processing are proposed. Two mathematical frameworks and algorithms to accomplish the watermarking of quantum images, authentication of ownership of already watermarked images and recovery of their unmarked versions on quantum computers are proposed. Encoding the images as 2n-sized normalised Flexible Representation of Quantum Images (FRQI) states, with n-qubits and 1-qubit dedicated to capturing the respective information about the colour and position of every pixel in the image respectively, the proposed algorithms utilise the flexibility inherent to the FRQI representation, in order to confine the transformations on an image to any predetermined chromatic or spatial (or a combination of both) content of the image as dictated by the watermark embedding, authentication or recovery circuits. Furthermore, by adopting an apt generalisation of the criteria required to realise physical quantum computing hardware, three standalone components that make up the framework to prepare, manipulate and recover the various contents required to represent and produce movies on quantum computers are also proposed. Each of the algorithms and the mathematical foundations for their execution were simulated using classical (i.e., conventional or non-quantum) computing resources, and their results were analysed alongside other longstanding classical computing equivalents. The work presented here, combined together with the extensions suggested, provide the basic foundations towards effectuating secure and efficient classical-like image and video processing applications on the quantum-computing framework. Full article
(This article belongs to the Special Issue Quantum Information 2012)
Figures

Open AccessReview On the Entropy of a Class of Irreversible Processes
Entropy 2013, 15(8), 2975-2988; doi:10.3390/e15082975
Received: 19 April 2013 / Revised: 5 June 2013 / Accepted: 9 July 2013 / Published: 26 July 2013
Cited by 2 | PDF Full-text (242 KB) | HTML Full-text | XML Full-text
Abstract
We review a recent technique for determining the entropy change accompanying certain classes of irreversible processes involving changes in the state of a system anchored to a reservoir. Time is introduced as a parameter to specify the corresponding entropy evolution of the system.
[...] Read more.
We review a recent technique for determining the entropy change accompanying certain classes of irreversible processes involving changes in the state of a system anchored to a reservoir. Time is introduced as a parameter to specify the corresponding entropy evolution of the system. The procedural details are outlined and their relation to the standard treatment of irreversible processes is examined. Full article
(This article belongs to the Special Issue Entropy and the Second Law of Thermodynamics)

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