Entropy Function Research Articles

Dynamical and thermodynamical stability of a charged thin-shell wormhole

AbstractA study of the dynamical and thermodynamical stability of a charged thin-shell wormhole built by gluing two Reissner–Nordström geometries is presented. The charge on the shell is linearly related to the matter content. For the dynamical stability, a concise inequality is obtained, valid for any barotropic equation of state that relates the pressure with the energy density at the throat. A thermodynamical description of the system is introduced, which leads to the temperature and the electric potentials. Adopting a linear equation of state for the pressure and a definite form for the entropy function, the set of equilibrium configurations that are both dynamically and thermodynamically stable is found.

Pseudoentropy sum rule by analytical continuation of the superposition parameter

Abstract In this paper, we establish a sum rule that connects the pseudoentropy and entanglement entropy of the superposition state. Through analytical continuation of the superposition parameter, we demonstrate that the transition matrix and density matrix of the superposition state can be treated in a unified manner. Within this framework, we naturally derive sum rules for the (reduced) transition matrix, pseudo-Rényi entropy, and pseudoentropy. Furthermore, we demonstrate the close relationship between the sum rule for pseudoentropy and the singularity structure of the entropy function for the superposition state after analytical continuation. We also explore potential applications of the sum rule, including its relevance to understanding the gravity dual of non-Hermitian transition matrices and establishing upper bounds for the absolute value of pseudoentropy.

Speed prediction and nearby road impact analysis using machine learning and ensemble of explainable AI techniques

Traffic speed prediction is an important topic in Intelligent Transport Systems (ITS). Although traffic speed prediction for real-life applications is burgeoning, the study of explaining and interpreting AI-based speed prediction is still in its initial stage. In this paper, we applied multiple advanced regression techniques, such as XGBoost and CatBoost optimized gradient boosting, Random Forest, and LASSO to predict traffic speed more accurately in the subsequent time windows. The experiment with prediction methods was conducted using the traffic speed data of the Seoul metropolitan road network. Each road segment represented as a node in the network is associated with neighboring roads within a configurable range. We picked heavily congested nodes as prediction targets. Then, we evaluated nearby road influences to determine critical contributions to the situation of the target nodes. We interpreted the model’s output and extracted the topmost influential neighboring nodes by using an ensemble of explainable artificial intelligence (XAI) techniques such as feature importance assessment using the GINI entropy function, Recursive Feature Elimination, Shapely Additive Explanation, and a method of measuring the impact of masked nodes. We validated the XAI interpretations through traffic flow simulation by tuning the topmost influential nearby roads’ speed and observing the effect on the roads’ traffic congestion relief correspondingly. We also proved our solution through local explanation techniques such as Local Interpretable Model-Agnostic Explanations. Our methods are applicable to any transport network and open the door to new strategies for controlling the specific nearby roads for effective congestion relief.

Holographic bounce cosmological models induced by viscous dark fluid from a generalized non-singular entropy function

Bounce cosmological models containing a dark viscous fluid in a spatially flat Friedmann–Robertson–Walker (FRW) universe are considered. The universe’s evolution is described in terms of generalized equation of state (EoS) parameters, in the presence of the bulk viscosity. Entropic cosmology plays a key role in the discussion, and the matter bounce behavior is described based on a nonsingular, generalized entropy function, recently proposed by S. D. Odintsov and T. Paul. Three different forms of the scale factor are investigated: an exponential, a power-law and a double-exponential function, respectively. Appropriate bounce cosmological models are formulated, via the relevant parameters of the modified EoS, and analytical expressions for the corresponding infrared cut-off are obtained, via the particle horizon. Results are displayed in holographic form, making use of generalized holographic cut-offs first introduced by S. Nojiri and S. D. Odintsov. In addition, the viability of the corresponding bounce cosmological models is investigated, taking into account the actual thermodynamic properties of our universe, by means of a no-singular, generalized entropy function. In the asymptotic case, an expression for the generalized entropy is obtained, which remarkably has the additivity property.

Thermo-Magnetic properties of non-relativistic particles under the effect of energy-dependent Hellmann potential

This manuscript presents an analysis of the thermal and magnetic properties of particles moving in two dimensions under the influence of an external magnetic field and Aharanov-Bohm flux, considering an energy-dependent Hellmann potential. The energy eigenvalue is obtained using the asymptotic iteration method. Next, we model the system as a canonical ensemble and derive the partition function to acquire analytical expressions for the Helmholtz free energy, entropy, mean energy, and specific heat. We observe that an increase in the external magnetic field and AB flux generally increases the energy eigenvalues, with a stronger effect at lower flux values, while energy eigenvalues decrease with an increase in the screening parameter. Additionally, Helmholtz free energy and entropy functions are sensitive to temperature, particularly in the low-temperature regime, while specific heat exhibits a Schottky anomaly. We also compute the magnetisation and susceptibility functions, finding that both magnetisation and susceptibility increase with the external magnetic field strength and the AB flux.

Assessing rural revitalization potential through rural transformation degree and sustainability: A quantitative study of 460 case villages in Lingbao, China

Extensive international experience shows that only villages with sustainable transformation achieve rural revitalization, while those with intense but unsustainable or stagnant transformation struggle to revitalize. However, this cognition lacks robust quantitative substantiation. Therefore, we established a rural revitalization potential assessment framework based on the rural transformation degree and sustainability, employing the Penalty for a Bottleneck (PFB) method and Entropy Function to measure the rural transformation degree and sustainability of 460 villages in Lingbao City, Henan Province, China, from 2000 to 2021, thus evaluating rural revitalization potential. The Mann-Kendall (MK) test was conducted to detect rural transformation thresholds, further quantifying the spatial relationship between rural transformation degree and sustainability through bivariate spatial autocorrelation analysis (BSA). Our findings resonate with the central place theory that villages near those at advanced stages of development struggle to transform sustainably. Additionally, with the optimization of rural population density, and land use structure, these villages demonstrated a discernible upward trajectory in transformation sustainability. Villages with the highest rural revitalization potential were predominantly distributed in the northern of the Yellow River terrace, while those in the southwestern mountainous areas lacked revitalization potential due to low transformation degree. Generally, villages at higher altitudes and steeper slopes exhibited lower rural transformation degree, sustainability, and revitalization potential. With 30 km as the critical point, rural revitalization potential decreased initially and then increased with distance from the county government seat. This study provides essential references for the rational allocation of rural transformation and revitalization resources and for optimizing rural development planning.

Statistical inference of entropy functions of generalized inverse exponential model under progressive type-II censoring test.

This article explores the estimation of Shannon entropy and Rényi entropy based on the generalized inverse exponential distribution under the condition of stepwise Type II truncated samples. Firstly, we analyze the maximum likelihood estimation and interval estimation of Shannon entropy and Rényi entropy for the generalized inverse exponential distribution. In this process, we use the bootstrap method to construct confidence intervals for Shannon entropy and Rényi entropy. Next, we select the gamma distribution as the prior distribution and apply the Lindley approximation algorithm to calculate `estimates of Shannon entropy and Rényi entropy under different loss functions including Linex loss function, entropy loss function, and DeGroot loss function respectively. Afterwards, simulation is used to calculate estimates and corresponding mean square errors of Shannon entropy and Rényi entropy in GIED model. The research results show that under DeGroot loss function, estimation accuracy of Shannon entropy and Rényi entropy for generalized inverse exponential distribution is relatively high, overall Bayesian estimation performs better than maximum likelihood estimation. Finally, we demonstrate effectiveness of our estimation method in practical applications using a set of real data.

Research on Evaluation of College-Classroom Teaching Quality Based on Pentapartitioned Neutrosophic Cubic Sets and Machine Vision

University-teaching quality evaluations are crucial for assessing teachers’ effectiveness and enhancing students’ learning in classrooms. To improve the evaluation efficiency, this study suggests a creative classroom evaluation approach by using machine vision and pentapartitioned neutrosophic cubic set (PNCS). First, this study uses machine vision technology to establish a PNCS to capture the students’ states in classrooms. Second, it proposes four entropy functions to determine the attribute weights. Third, it combines the improved entropy weight functions with the PNCS to evaluate the teaching effectiveness. This study’s practical price is to introduce big data theories into teaching evaluation fields. Last, an example is provided to confirm the efficacy and applicability of the evaluation approach suggested in this study.

On two classes of Rényi entropy functions of a quantum channel

On two classes of Rényi entropy functions of a quantum channel

Multidimensional Characterization and Separation of Ultrafine Particles: Insights and Advances by Means of Froth Flotation

Particle systems and their efficient and precise separation are becoming increasingly complex. Therefore, instead of focusing on a single separation feature, a multidimensional approach is needed where more than one particle property is considered. This, however, requires the precise characterization of the particle system, which is especially challenging for fine particles with sizes below 10 µm. This paper discusses the benefits and limitations of different characterization techniques, including optical contour analysis, inverse gas chromatography, flow cytometry, and SEM-based image analysis. The separation of ultrafine particles was investigated for a binary system using froth flotation, where a novel developed flotation apparatus is used. A special focus was placed on the multidimensional evaluation of the separation according to the particle properties of size, shape, and wettability, which was addressed via multivariate Tromp and entropy functions. The results emphasize the intricacy of the flotation process and the complex interaction of the individual particle properties and process parameters. The investigations contribute to the understanding of the characterization of particulate properties as well as the separation behavior of ultrafine particles via froth flotation, especially in the case of a multidimensional approach.

Different Aspects of Entropic Cosmology

We provide a short review of the recent developments in entropic cosmology based on two thermodynamic laws of the apparent horizon, namely the first and the second laws of thermodynamics. The first law essentially provides the change in entropy of the apparent horizon during the cosmic evolution of the universe; in particular, it is expressed by TdS=−d(ρV)+WdV (where W is the work density and other quantities have their usual meanings). In this way, the first law actually links various theories of gravity with the entropy of the apparent horizon. This leads to a natural question—“What is the form of the horizon entropy corresponding to a general modified theory of gravity?”. The second law of horizon thermodynamics states that the change in total entropy (the sum of horizon entropy + matter fields’ entropy) with respect to cosmic time must be positive, where the matter fields behave like an open system characterised by a non-zero chemical potential. The second law of horizon thermodynamics importantly provides model-independent constraints on entropic parameters. Finally, we discuss the standpoint of entropic cosmology on inflation (or bounce), reheating and primordial gravitational waves from the perspective of a generalised entropy function.

Partially invariant solution with an arbitrary surface of blow-up for the gas dynamics equations admitting pressure translation

We applied a method of symmetry reduction to the gas dynamics equations with a special form of the equation of state. This equation of state is a pressure represented as the sum of a density and an entropy functions. The symmetry Lie algebra of the system is 12-dimensional. One, two and three-dimensional subalgebras were considered. In this article, four-dimensional subalgebras are considered for the first time. Specifically, invariants are calculated for 50 four-dimensional subalgebras. Using invariants of one of the subalgebras, a symmetry reduction of the original system is calculated. The reduced system is a partially invariant submodel because one gas-dynamic function cannot be expressed in terms of the invariants. The submodel leads to two families of exact solutions, one of which describes the isochoric motion of the media, and the other solution specifies an arbitrary blow-up surface. For the first family of solutions, the particle trajectories are parabolas or rays; for the second family of solutions, the particles move along cubic parabolas or straight lines. From each point of the blow-up surface, particles fly out at different speeds and end up on a straight line at any other fixed moment in time. A description of the motion of particles for each family of solutions is given.

Statistical uncertainty principle in Markov kinetics

A reciprocality between the statistical variance of observables of a thermodynamic state and that of their conjugate variables, as entropic forces, originates from the thermodynamic conjugacy with respect to an entropy function. This thermodynamic uncertainty principle in equilibrium can be derived from the Maximum Entropy principle and is independent upon underlying mechanistic details. We present, based on the Maximum Caliber principle as the dynamic generalization of Maximum Entropy, the formalism of the uncertainty principle in kinetics in time homogeneous Markov processes between transitional observables and their conjugate path entropic forces. A stochastic biophysical model for molecular motors is used as an illustrating example. The present work generalizes the phenomenological thermodynamics of uncertainties/fluctuations and is applicable to data ad infinitum.

Quasi-uniform entropy vs topological entropy

In 2023 Haihambo and Olela Otafudu introduced and studied the notion of quasi-uniform entropy hQU(ψ) for a uniformly continuous self-map ψ of a quasi-metric or a quasi-uniform space X. In this paper, we discuss the connection between the topological entropy functions h,hf and the quasi-uniform entropy function hQU on a quasi-uniform space X, where h and hf are the topological entropy functions defined using compact sets and finite open covers, respectively. In particular, we have shown that for a uniformly continuous self-map ψ of a T0-quasi-uniform space (X,U) we have h(ψ)≤hQU(ψ) when X is compact and hQU(ψ)≤hf(ψ) with equality if X is a compact T2 space.

Action, entropy and pair creation rate of charged black holes in de Sitter space

We compute and clarify the interpretation of the on-shell Euclidean action for Reissner-Nordström black holes in de Sitter space. We show the on-shell action is minus the sum of the black hole and cosmological horizon entropy for arbitrary mass and charge in any number of dimensions. This unifying expression helps to clear up a confusion about the Euclidean actions of extremal and ultracold black holes in de Sitter, as they can be understood as special cases of the general expression. We then use this result to estimate the probability for the pair creation of black holes with arbitrary mass and charge in an empty de Sitter background, by employing the formalism of constrained instantons. Finally, we suggest that the decay of charged de Sitter black holes is governed by the gradient flow of the entropy function and that, as a consequence, the regime of light, superradiant, rapid charge emission should describe the potential decay of extreme charged Nariai black holes to singular geometries.

Singularity properties of the entropy in an enclosed system characterized by accumulated noise stochastic processes

Due to the irreversibility of processes in an enclosed system, the randomness in the system increases in time and can be represented by an accumulated noise stochastic process. In contrast to the thermodynamics theory, the analysis of the system is based on the information theory point of view. The system is defined by two states: a time state and a timeless state. Based on the central limit theorem, due to the additivity of the noise process, the time state is characterized by the time-dependent Gaussian stochastic process. In contrast to Shannon's theory, precise expressions for the probability density, information, and entropy functions of the random variables defining the time-dependent process are derived and analyzed for a finite, infinite, and zero value of the related time-dependent variance. It has been proven that the entropy rate is not necessarily inversely proportional to time, as presented in previous works. Furthermore, mathematical proofs are presented, showing that the system entropy is a singularity function that increases towards infinity in the time state and then drops to zero value when the system enters the timeless state. The timeless state is characterized by the undefined pdf function, infinite values of information, and zero entropy.

Analytical solution for Ξ-type qutrit interacting nonlinearly with a cavity field through Kerr-like medium with intrinsic noise present

This paper presents an analytical solution for the Milburn equation describing the interaction between a 3-level atom in a [Formula: see text]-configuration, a cavity field, and a nonlinear Kerr-like medium. The Hamiltonian of the model is presented in the rotating wave approximation (RWA) under specific conditions. The obtained analytical solution accounts for the impact of intrinsic decoherence and nonlinear terms on the dynamics of various physical phenomena. Specifically, we explore the behavior of atomic population, entropy functions, entanglement, negativity, and correlation, highlighting their dependence on the physical parameters of the [Formula: see text]-level atom-cavity system.

Improved protocols for secure multiplication using secret sharing scheme

Herein, we present a secure multiplication method that uses secret sharing to solve the security problems presented by Watanabe et al. We implemented the characteristics of the exponent operation in which the product of two numbers with the same base (in this case, the primitive element) involves only the addition of their exponents. In contrast to typical secret sharing schemes, our proposed model requires two shares to be sent to each server simultaneously to achieve multiplication without increasing the number of servers required, thereby resulting in a lower cost of establishing a physical server. In addition, Shannon’s entropy function was used to describe the security of the proposed method. Finally, we evaluated our proposed method in terms of computational and communication costs.

New Inequalities for Entropy Function

New Inequalities for Entropy Function

A Time-Series Feature-Extraction Methodology Based on Multiscale Overlapping Windows, Adaptive KDE, and Continuous Entropic and Information Functionals

We propose a new methodology to transform a time series into an ordered sequence of any entropic and information functionals, providing a novel tool for data analysis. To achieve this, a new algorithm has been designed to optimize the Probability Density Function (PDF) associated with a time signal in the context of non-parametric Kernel Density Estimation (KDE). We illustrate the applicability of this method for anomaly detection in time signals. Specifically, our approach combines a non-parametric kernel density estimator with overlapping windows of various scales. Regarding the parameters involved in the KDE, it is well-known that bandwidth tuning is crucial for the kernel density estimator. To optimize it for time-series data, we introduce an adaptive solution based on Jensen–Shannon divergence, which adjusts the bandwidth for each window length to balance overfitting and underfitting. This solution selects unique bandwidth parameters for each window scale. Furthermore, it is implemented offline, eliminating the need for online optimization for each time-series window. To validate our methodology, we designed a synthetic experiment using a non-stationary signal generated by the composition of two stationary signals and a modulation function that controls the transitions between a normal and an abnormal state, allowing for the arbitrary design of various anomaly transitions. Additionally, we tested the methodology on real scalp-EEG data to detect epileptic crises. The results show our approach effectively detects and characterizes anomaly transitions. The use of overlapping windows at various scales significantly enhances detection ability, allowing for the simultaneous analysis of phenomena at different scales.