Entropy Space Research Articles

Nano‐High Entropy Materials in Electrocatalysis

AbstractHigh entropy materials (HEMs) compositing of at least five elements have gained widespread attention in the field of electrocatalysis due to their tunable activities and high stability. These intrinsic properties can be further highlighted when the size of HEMs comes to the nanoscale. In nanostructured HEMs, the fascinating properties including large composition space, multi‐element synergy, and high configuration entropy are expected to endow nano‐HEMs with excellent catalytic activity and stability, thus providing greater potential for the design of advanced electrocatalysts. In this review, nano‐HEMs are differentiated in detail in dimensions and the common synthesis methods are summarized. Additionally, from the perspective of the complex nanostructure‐performance relationship, the applications of nano‐HEMs in electrocatalysis systems, including water‐splitting (hydrogen evolution reaction (HER), oxygen evolution reaction (OER)), hydrogen oxidation reaction (HOR), oxygen reduction reaction (ORR), carbon dioxide reduction reaction (CO2RR), nitrogen reduction reaction (NRR) and alcohol oxidation reaction (AOR) are discussed. Finally, the main challenges faced by nano‐HEMs electrocatalysis are underscored. This review is expected to provide more insights into understanding and developing efficient electrocatalytic materials for practical applications.

Optimizing Distributions for Associated Entropic Vectors via Generative Convolutional Neural Networks.

The complete characterization of the almost-entropic region yields rate regions for network coding problems. However, this characterization is difficult and open. In this paper, we propose a novel algorithm to determine whether an arbitrary vector in the entropy space is entropic or not, by parameterizing and generating probability mass functions by neural networks. Given a target vector, the algorithm minimizes the normalized distance between the target vector and the generated entropic vector by training the neural network. The algorithm reveals the entropic nature of the target vector, and obtains the underlying distribution, accordingly. The proposed algorithm was further implemented with convolutional neural networks, which naturally fit the structure of joint probability mass functions, and accelerate the algorithm with GPUs. Empirical results demonstrate improved normalized distances and convergence performances compared with prior works. We also conducted optimizations of the Ingleton score and Ingleton violation index, where a new lower bound of the Ingleton violation index was obtained. An inner bound of the almost-entropic region with four random variables was constructed with the proposed method, presenting the current best inner bound measured by the volume ratio. The potential of a computer-aided approach to construct achievable schemes for network coding problems using the proposed method is discussed.

Information entropy in spin–orbit coupled dipolar condensates with magnetic field

In this paper, we study the formation of Shannon information entropy in spin–orbit coupled (SOC) spin-1 antiferromagnetic dipolar Bose–Einstein condensates with external magnetic field. Our results show that, in the absence of magnetic field and with an increase in dipole–dipole interaction (DDI), information entropy in position space [Formula: see text] and momentum space [Formula: see text] remains almost unchanged and increases, respectively. Meanwhile, the order parameter [Formula: see text] decreases, which implies that the system develops toward a disorder state. With the increase of SOC strength, [Formula: see text], [Formula: see text] and [Formula: see text] show similar dynamics behavior. Whereas, in the presence of magnetic field, [Formula: see text] and [Formula: see text] are localized in the small scope by increasing the dipole and SOC strength. In addition, the value of [Formula: see text] is nearly the same in this process. These results embody that the introduction of external magnetic field suppresses the role of SOC and DDI, and impedes the condensates towards disorder state. At last, the influence of geometric structure and atom number on information entropy is investigated. It is seen that a narrower trap and fewer atom number make [Formula: see text] decrease and [Formula: see text] increase.

Holographic vacuum energy regularization and corrected entropy of de Sitter space

Abstract We propose that the spectrum of the surface area of the apparent horizon (AH) of de Sitter (dS) spacetime leads to corrected temperature and entropy of the dS spacetime, offering new insights into its thermodynamic properties. This is done by employing the spectrum of the AH radius, acquired from the Wheeler--DeWitt (WDW) equation, together with the Stefan--Boltzmann law, the time-energy uncertainty relation, and the unified first law of thermodynamics.

Computational experiments with cellular-automata generated images reveal intrinsic limitations of convolutional neural networks on pattern recognition tasks

The extraordinary success of convolutional neural networks (CNNs) in various computer vision tasks has revitalized the field of artificial intelligence. The out-sized expectations created by this extraordinary success have, however, been tempered by a recognition of CNNs’ fragility. Importantly, the magnitude of the problem is unclear due to a lack of rigorous benchmark datasets. Here, we propose a solution to the benchmarking problem that reveals the extent of the vulnerabilities of CNNs and of the methods used to provide interpretability to their predictions. We employ cellular automata (CA) to generate images with rigorously controllable characteristics. CA allow for the definition of both extraordinarily simple and highly complex discrete functions and allow for the generation of boundless datasets of images without repeats. In this work, we systematically investigate the fragility and interpretability of the three popular CNN architectures using CA-generated datasets. We find a sharp transition from a learnable phase to an unlearnable phase as the latent space entropy of the discrete CA functions increases. Furthermore, we demonstrate that shortcut learning is an inherent trait of CNNs. Given a dataset with an easy-to-learn and strongly predictive pattern, CNN will consistently learn the shortcut even if the pattern occurs only on a small fraction of the image. Finally, we show that widely used attribution methods aiming to add interpretability to CNN outputs are strongly CNN-architecture specific and vary widely in their ability to identify input regions of high importance to the model. Our results provide significant insight into the limitations of both CNNs and the approaches developed to add interpretability to their predictions and raise concerns about the types of tasks that should be entrusted to them.

Pseudo-random number generation based on spatial chaotic map of Logistic type and its cryptographic application

The pseudo-random number generator (PRNG) based on chaos has been widely used in the fields of digital communication, cryptography and computer simulation. In this paper, we study a new PRNG based on spatial surface chaotic system (SSCS), which is constructed based on coupling mapping lattice (CML) and one-dimensional Logistic chaotic map. To verify the performance of this generator, we study its nonlinear dynamic properties, including the Lyapunov exponent, ergodicity and bifurcation phenomena. Moreover, we analyze the cryptographic properties such as key space, key sensitivity, correlation, histogram and information entropy, while performing NIST SP800-22 test and TestU01 test for the randomness of this system. Theoretical analysis and numerical simulation results show that the PRNG proposed in this paper has good complexity, ergodicity, sensitivity and randomness. Moreover, the key space can increase dynamically with the increase of encrypted data, especially suitable for the protection of big data such as multimedia, which is more advantageous than most existing chaotic mapping. The results of this paper will provide a new idea for the study of chaotic cryptography, and motivate the study of new discrete chaotic models with desirable statistical properties.

EFE-LSTM: A Feature Extension, Fusion and Extraction Approach Using Long Short-Term Memory for Navigation Aids State Recognition

Navigation aids play a crucial role in guiding ship navigation and marking safe water areas. Therefore, ensuring the accurate and efficient recognition of a navigation aid’s state is critical for maritime safety. To address the issue of sparse features in navigation aid data, this paper proposes an approach that involves three distinct processes: the extension of rank entropy space, the fusion of multi-domain features, and the extraction of hidden features (EFE). Based on these processes, this paper introduces a new LSTM model termed EFE-LSTM. Specifically, in the feature extension module, we introduce a rank entropy operator for space extension. This method effectively captures uncertainty in data distribution and the interrelationships among features. The feature fusion module introduces new features in the time domain, frequency domain, and time–frequency domain, capturing the dynamic features of signals across multiple dimensions. Finally, in the feature extraction module, we employ the BiLSTM model to capture the hidden abstract features of navigational signals, enabling the model to more effectively differentiate between various navigation aids states. Extensive experimental results on four real-world navigation aid datasets indicate that the proposed model outperforms other benchmark algorithms, achieving the highest accuracy among all state recognition models at 92.32%.

Particle in a Markov Cube by the Non-Classical Information Entropy Space

Particle in a Markov Cube by the Non-Classical Information Entropy Space

A Tiling Method for Sub-Arrayed Spherical Conformal Phased Array Antennas Based on Maximum 3-D Space Entropy Model

A Tiling Method for Sub-Arrayed Spherical Conformal Phased Array Antennas Based on Maximum 3-D Space Entropy Model

Quench dynamics of a Tonks-Girardeau gas in one dimensional anharmonic trap

The quench dynamics of strongly interacting bosons on quartic and sextic traps are studied by exactly solving the time-dependent many-boson Schrödinger equation numerically. The dynamics are addressed by the key measures of one-body density in conjugate space and information entropy. For both cases, rich many-body dynamics are exhibited and the loss of the Bose–Fermi oscillation in the Tonks–Girardeau limit is also attributed.

Optimization method of 3D reconstruction of metal cultural relics based on 3D laser scanning data reduction

AbstractThe extraction effect and feature matching are poor in the three‐dimensional reconstruction of metal cultural relics, which leads to a poor reconstruction effect. Therefore, an optimization method of three‐dimensional reconstruction of metal cultural relics based on 3D laser scanning data reduction is proposed. The overall technical design route of the method is shown as follows. Based on this model, the 3D laser scanning method is used to collect 3D images of metal artefacts, combined with colour space and 2D entropy detection methods to pre‐process 3D images, and feature matching of point clouds is carried out to extract and optimize the significant value of superpixels, and a 3D reconstructed visual model is constructed. Affine transformation is used to obtain the affine invariant moment of the structural light parameters of the visual feature lines of metal cultural relics. The light stability adjustment of the three‐dimensional reconstruction of metal cultural relics is realized by using the linear structural light adjustment method in the HSV colour space. The rigid and non‐rigid registration methods are introduced to match the point cloud. The product quantization algorithm is used to linearize the error function, and the block feature detection and matching model of spatial image is obtained. The noise number is judged by the threshold value, and the three‐dimensional reconstruction technology is combined to realize the three‐dimensional reconstruction of metal relics. The simulation results show that this method has good visual expression ability, high feature recognition rate, and improves the three‐dimensional reconstruction ability of metal relics.

Macroscopic model and statistical model to characterize electromagnetic information of a digital coding metasurface.

A digital coding metasurface is a platform connecting the digital space and electromagnetic wave space, and has therefore gained much attention due to its intriguing value in reshaping wireless channels and realizing new communication architectures. Correspondingly, there is an urgent need for electromagnetic information theory that reveals the upper limit of communication capacity and supports the accurate design of metasurface-based communication systems. To this end, we propose a macroscopic model and a statistical model of the digital coding metasurface. The macroscopic model uniformly accommodates both digital and electromagnetic aspects of the meta-atoms and predicts all possible scattered fields of the digital coding metasurface based on a small number of simulations or measurements. Full-wave simulations and experimental results show that the macroscopic model is feasible and accurate. A statistical model is further proposed to correlate the mutual coupling between meta-atoms with covariance and to calculate the entropy of the equivalent currents of digital coding metasurface. These two models can help reconfigurable intelligent surfaces achieve more accurate beamforming and channel estimation, and thus improve signal power and coverage. Moreover, the models will encourage the creation of a precoding codebook in metasurface-based direct digital modulation systems, with the aim of approaching the upper limit of channel capacity. With these two models, the concepts of current space and current entropy, as well as the analysis of information loss from the coding space to wave space, is established for the first time, helping to bridge the gap between the digital world and the physical world, and advancing developments of electromagnetic information theory and new-architecture wireless systems.

Influence of geometric structure on information entropy in spin-1 ferromagnetic dipolar Bose–Einstein condensates

In this study, we investigate the dynamics properties of spin-1 ferromagnetic Bose–Einstein condensates (BECs) with dipole–dipole interaction (DDI). Numerical results are obtained by solving the mean-field nonlocal Gross–Pitaevskii equation. We find that the population of the information entropy in momentum space [Formula: see text] is greatly affected by geometric structure and dipole strength. The prolate condensate is favorable to obtain bigger [Formula: see text] than oblate condensate. The density distribution verifies that the formation of magnetic domain is associated with the variation of [Formula: see text]. In addition, the kinetic energy displays that dramatical oscillation appears for strong dipolar interaction and it is larger in prolate condensate. Also, we use the order parameter to describe the order–disorder crossover. It is shown that BECs develop toward the disordered state with prolate condensate under strong DDI.

Depicting Defects in Metallic Glasses by Atomic Vibrational Entropy.

Due to the chaotic structure of amorphous materials, it is challenging to identify defects in metallic glasses. Here we tackle this problem from a thermodynamic point of view using atomic vibrational entropy, which represents the inhomogeneity of atomic contributions to vibrational modes. We find that the atomic vibrational entropy is correlated to the vibrational mean-square displacement and polyhedral volume of atoms, revealing the critical role of vibrational entropy in bridging dynamics, thermodynamics, and structure. On this method, the local vibrational entropy obtained by coarse-graining the atomic vibrational entropy in space can distinguish more effectively between liquid-like and solid-like atoms in metallic glasses and establish the correlation between the local vibrational entropy and the structure of metallic glasses, offering a route to predict the plastic events from local vibrational entropy. The local vibration entropy is a good indicator of thermally activated and stress-driven plastic events, and its predictive ability is better than that of the structural indicators.

Late-time correlators and complex geodesics in de Sitter space

We study two-point correlation functions of a massive free scalar field in de Sitter space using the heat kernel formalism. Focusing on two operators in conjugate static patches we derive a geodesic approximation to the two-point correlator valid for large mass and at late times. This expression involves a sum over two complex conjugate geodesics that correctly reproduces the large-mass, late-time limit of the exact two-point function in the Bunch-Davies vacuum. The exponential decay of the late-time correlator is associated to the timelike part of the complex geodesics. We emphasize that the late-time exponential decay is in tension with the finite maximal entropy of empty de Sitter space, and we briefly discuss how non-perturbative corrections might resolve this paradox.

PointerScope: Understanding Pointer Patching for Code Randomization

Various fine-grained randomization schemes have been designed to increase the entropy of process space, while none of them can rise from an academic exercise to industrial deployment like Address Space Layout Randomization (ASLR). One of the critical reasons is the incorrectness of randomization caused by the mismatch between their pointer collection capabilities and the high accuracy requirements of the pointer patching task. In this article, we present PointerScope, an accurate compile-time pointer collection scheme deriving from a group of novel observations. The success of PointerScope relies on the complete tracing of the pointer generation process, including the compilation chain from compiler to static linker and the interface specification between them. From this view, PointerScope identifies four types of pointer-related static linker behaviors and clarifies five types of inherent addressing modes in the x86-64 architecture. The vague understanding of them causes the Compiler-assisted Code Randomization (CCR) to incorrectly collect pointers and patch them to the wrong values after randomization. Further, we measure the pointer collection capability of augmented binary analysis, the experimental results show that they can mitigate challenges from the traditional binary analysis by the given premises, but additional heuristics still need to be designed to support the fine-grained randomization.

Timelike entanglement entropy

We define a new complex-valued measure of information called the timelike entanglement entropy (EE) which in the boundary theory can be viewed as a Wick rotation that changes a spacelike boundary subregion to a timelike one. An explicit definition of the timelike EE in 2d field theories is provided followed by numerical computations which agree with the analytic continuation of the replica method for CFTs. We argue that timelike EE should be correctly interpreted as another measure previously considered, the pseudo entropy, which is the von Neumann entropy of a reduced transition matrix. Our results strongly imply that the imaginary part of the pseudo entropy describes an emergent time which generalizes the notion of an emergent space from quantum entanglement. For holographic systems we define the timelike EE as the total complex valued area of a particular stationary combination of both space and timelike extremal surfaces which are homologous to the boundary region. For the examples considered we find explicit matching of our optimization procedure and the careful implementation of the Wick rotation in the boundary CFT. We also make progress on higher dimensional generalizations and relations to holographic pseudo entropy in de Sitter space.

Linear response of entanglement entropy to Toverline{T} in massive QFTs

We compute the leading correction to entanglement entropy in Toverline{T} deformed massive QFTs. We show that both for massive scalar and Dirac fermion, the leading order correction to the entanglement entropy of half space comes from the boundary of the entangling surface. For the case of massive scalar, the boundary term is finite while for massive fermion, it diverges logarithmically giving rise to an additional log-square divergence in the entanglement entropy.

Information theoretic measures on the two-photon transitions of hydrogen atom embedded in weakly coupled plasma environment

The quantum information theoretic measures in terms of Shannon entropy and Fisher entropy (both in position and momentum spaces) on the ground, excited as well as virtual states arising out of the two-photon transitions (1s → nl; n = 2 − 4, l = 0, 2) of H atom embedded in classical weakly coupled plasma environment are done for the first time. Fourth order time dependent perturbation theory is adopted within a variational framework for calculating the two photon excitation energies and their respective wavefunctions from an analysis of the pole positions of the non linear response of the system. The representation of virtual state follows from an analysis of the linear response at such poles using a novel method developed by us. Ground and perturbed state wave functions of appropriate symmetries are represented by linear combination of Slater-type orbitals. The analytic form of the momentum space wave functions of ground, excited and virtual states are determined by taking Fourier transformation of the respective position space wave functions. The quantum information measures give interesting insights on the delocalization patterns of the all the real and virtual states under question w.r.t. the increase in plasma strength. The estimated data values are found to be in excellent agreement with the few existing in literature for the ground as well as excited states participating in the two-photon transitions. Such data for the virtual states are completely new and can be set as benchmark for future works in related disciplines.

A class of m-dimension grid multi-cavity hyperchaotic maps and its application

In this paper, a new closed-loop multiple modulation coupling (CMMC) method is proposed to construct an enhanced chaotic system. Based on the iterative chaotic map with infinite collapse (ICMIC) and Sinusoidal map, a class of hyperchaotic maps are constructed, and a new 3D-Hourglass chaotic map is proposed. Dynamics analyses show that the proposed systems have 3 positive Lyapunov exponents (LEs), large maximum Lyapunov exponents (MLE) and parameter space, good randomness, and high permutation entropy (PE) complexity. Interestingly, the original system exists lots of multiple coexistence attractor rings. In addition, the grid multi-cavity chaotic model of 3D-Hourglass is designed by using nonlinear hyperbolic tangent function, which significantly expands the phase space, and makes the translation control of the cavity smoother. Multi-cavity hyperchaotic map maintains the high complexity and rich dynamics of the original system. Finally, we implement it on DSP, and design Pseudorandom Number Generator (PRNG) as its applications.