Statistical Entropy Research Articles

Concentration and cavitation in the Riemann solutions to the Umami Chaplygin Euler equations

The concentration phenomena in fluid dynamics can be mathematically described by delta-shocks. With the introduction of flux-function, the Riemann problem for the Euler system with Umami Chaplygin gas equation of state is discussed. What Umami Chaplygin gas means is that the fluid obeys the pressure–density relation where the pressure is negative and is a new generalization of Chaplygin gas. The solutions with six kinds of structures are constructed. Unlike the Chaplygin gas, the delta-shock occurs in solutions, even though the system is strictly hyperbolic and two characteristic fields are genuinely nonlinear. The generalized Rankine–Hugoniot relation and entropy condition for delta-shock are clarified. Additionally, the phenomena of concentration and cavitation and the formation of delta-shocks and vacuum states in solutions are identified and analyzed as the Umami Chaplygin gas pressure and flux-function vanish simultaneously. It is proved that as the pressure and flux-function drop to zero, any solution consisting of two shocks tends to the delta-shock solution of the pressureless Euler system, and any solution consisting of two rarefaction waves tends to the vacuum Riemann solution of the pressureless Euler system. Finally, some numerical results exhibiting the processes of formation of delta-shocks and vacuum states are presented.

Numerical analysis of flow and heat transfer characteristics in Taylor-Couette-Poiseuille flow utilizing Large Eddy Simulation method

The flow and heat transfer characteristics within the Taylor-Couette-Poiseuille configuration induced by supercritical carbon dioxide flowing through the gap between the turbine shaft and the stationary casing were studied using Large Eddy Simulation. Wavelet analysis was used to calculate pressure fluctuations across various frequencies. Computational assessments were carried out to evaluate changes in the field synergy angle and inertial perturbations within the annular gap. A new theory was introduced to seamlessly integrate temperature, pressure, and velocity fields. Additionally, entropy generation in the Taylor-Couette-Poiseuille flow regime was thoroughly examined. The study revealed the emergence of vortices at the rotating wall, indicating a dynamic process in which large-scale vortices dissolve and more minor ones form. As frequency increases, pressure fluctuations grow. Increasing the mass flow rate can reduce the twisting vortex at the rotating wall and delay the onset of temperature fluctuations. Additionally, increasing the mass flow rate enhances the cooling effect on the rotating shaft. In the radial direction, as r increases, the field synergy angle and the inertial disturbance both show a trend of first decreasing and then increasing. The heat transfer performance is best when r = 0.6 and decreases significantly when r = 0.95. The synergy between the temperature gradient field, pressure gradient field, and velocity field shows a trend opposite to the field synergy angle and the inertial disturbance. As one moves from the rotating wall toward the stationary wall, temperature and velocity entropy production rates decrease, with noticeable fluctuations near the rotating wall.

Numerical illustration using finite difference method for the transient flow through porous microchannel and statistical interpretation of entropy using response surface methodology

The current article discloses the influence of the hyperbolic tangent nanofluid on time dependent flow through a microchannel when a magnetic field is applied. The porous medium was incorporated using the Darcy–Forchheimer model. The chemical reaction is explained by Arrhenius activation energy. Temperature is determined by convective boundary conditions. The irreversibility occurring in the flow is analyzed. The modeled problem gives rise to partial differential equations, which are computed by finite difference method. Response surface methodology, an optimization technique, is used to attain the optimal conditions for entropy generated for the flow of fluid. Results of the analysis reveal that concentration decreases with the rise in reaction rate parameter and increases with activation energy parameter. Prandtl and Eckert numbers, with their increase, enhance entropy, and fluid friction irreversibility is at its highest. Perfect co-relation is attained for the model by the response surface methodology, with a co-relation coefficient of 100 %. The Weissenberg number is highly sensitive to change in the present modeling, followed by Darcy and Reynolds numbers. The Reynolds number and Darcy number show positive sensitivity, while the Weissenberg number shows negative sensitivity to the entropy generated.

Potential Benefits and Challenges of Quantifying Pseudoreplication in Genomic Data with Entropy Statistics.

Generating vast arrays of genetic markers for evolutionary ecology studies has become routine and cost-effective. However, analyzing data from large numbers of loci associated with a small number of finite chromosomes introduces a challenge: loci on the same chromosome do not assort independently, leading to pseudoreplication. Previous studies have demonstrated that pseudoreplication can substantially reduce precision of genetic analyses (and make confidence intervals wider), such as FST and linkage disequilibrium (LD) measures between pairs of loci. In LD analyses, another type of dependency (overlapping pairs of the same loci) also creates pseudoreplication. Building on previous work, we explore the potential of entropy metrics to improve the status quo, particularly total correlation (TC), to assess pseudoreplication in LD studies. Our simulations, performed on a monoecious population with a range of effective population sizes (Ne) and numbers of loci, attempted to isolate the overlapping-pairs-of-loci effect by considering unlinked loci and using entropy to quantify inter-locus relationships. We hypothesized a positive correlation between TC and the number of loci (L), and a negative correlation between TC and Ne. Results from our statistical models predicting TC demonstrate a strong effect of the number of loci, and muted effects of Ne and other predictors, adding support to the use of entropy-based metrics as a tool for estimating the statistical information of complex genetic datasets. Our results also highlight a challenge regarding scalability; computational limitations arise as the number of loci grows, making our current approach limited to smaller datasets. Despite these challenges, this work further refines our understanding of entropy measures, and offers insights into the complex dynamics of genetic information in evolutionary ecology research.

Thirring universe model

In recent years, there has been a significant amount of research focused on Thirring instantons. This study aims to employ the Thirring quantum model as a theoretical Universe model to gain a more profound understanding of the beginning of the Universe. For this, we propose to analyze the entropy of the quantum states of zero energy Thirring instanton solutions and the transition to other quantum states. Our findings by also using Lyapunov exponents and the cyclic attractors as comparative nonlinear methods show that there is no entropy corresponding to instanton solutions with zero energy and that the sudden increase in entropy indicates the formation of the Universe. We evaluate the implications of this study in terms of the standard Universe model. Thus we anticipate that these results have the potential to contribute significantly to our understanding of the origin of the Universe and highlight the role of chaos and complexity in its evolution.

Evaluation of steel metallurgical dust management: combining treatment methods and resource attributes

The escalating challenges of resource scarcity and environmental pressures have drawn significant attention to heavy metal-containing dust generated during steel production. While previous research on heavy metals in steel manufacturing has primarily focused on emission inventories, health and ecological risks, and recycling technologies, the assessment of steel metallurgical dust management has been largely overlooked. To address this research gap, this study employed statistical entropy analysis to evaluate the effectiveness of dust treatment in the steel production process, aiming to identify potential issues in dust management. Furthermore, an evaluation framework was established to systematically assess the resource attributes of steel metallurgical dust, thereby supporting evidence-based decision-making in dust management. Results indicate that Cd, Pb, As, Zn, Cr, and Hg tend to accumulate in dust during steel production. Given its high resource attribute, converter dust should be prioritized for recovery. Further analysis suggests that the rotary kiln process plays a transitional role in dust recovery. This study provides a scientific foundation for dust management in the steel industry and offers guidance for the sustainable development of dust utilization.

Delta-shocks and vacuums in Riemann solutions to the Umami Chaplygin Aw–Rascle model

This paper is concerned with the formation of delta-shocks and vacuum states for zero-pressure Euler equations. With the introduction of the Umami Chaplygin gas, the Riemann problem for Aw–Rascle model with the reasonable flux-function is solved analytically. The three kinds of Riemann solutions involving the delta-shock are obtained. The generalized Rankine–Hugoniot relation and entropy condition for delta-shock are clarified. Under the entropy condition, the existence and uniqueness of the delta-shock solution are established by solving the generalized Rankine–Hugoniot relation. It is rigorously shown that as the Umami Chaplygin gas pressure and flux-function approach to zero simultaneously, the Riemann solutions of the considered model converge to these of the zero-pressure Euler equations. The numerical results support the theoretical analysis in the end.

Shannon entropy in quasiparticle states of quantum chains

Abstract We investigate the Shannon entropy of the total system and its subsystems, as well as the subsystem Shannon mutual information, in quasiparticle excited states of free bosonic and fermionic chains and the ferromagnetic phase of the spin-1/2 XXX chain. For single-particle and double-particle states, we derive various analytical formulas for free bosonic and fermionic chains in the scaling limit. These formulas are also applicable to certain magnon excited states in the XXX chain in the scaling limit. We also calculate numerically the Shannon entropy and mutual information for triple-particle and quadruple-particle states in bosonic, fermionic, and XXX chains. We discover that Shannon entropy, unlike entanglement entropy, typically does not separate for quasiparticles with large momentum differences. Moreover, in the limit of large momentum difference, we obtain universal quantum bosonic and fermionic results that are generally distinct and cannot be explained by a semiclassical picture.

GRP – A direct Godunov extension

The classical paper [40] by S. K. Godunov had a revolutionary effect on the field of numerical simulations of compressible fluid flows. Yet, for some twenty years after its publication, it was mostly used by the mathematical community in the Soviet Union. The seminal paper of van Leer [85] has inaugurated the period of universal interest in high-resolution extensions of Godunov's scheme. The first step to take was to modify the (locally) self-similar solution to the Riemann Problem (at discontinuities) by allowing piecewise-polynomial (rather than piecewise-constant) initial data. The GRP (Generalized Riemann Problem) analysis [6] provided analytical solutions (for piecewise-linear data) that could be readily implemented in a high-resolution robust code. This review paper focuses on the evolution of some mathematical aspects of this method. It addresses the three concepts of consistency, stability and convergence in the context of compact finite difference (or finite volume) schemes for systems of nonlinear hyperbolic conservation laws. The treatment utilizes the framework of “balance laws”, a common viewpoint in relevant physical conservation laws. The first significant observation is that under very mild conditions a weak solution is indeed a solution to the balance law (obtained by a formal application of the Gauss-Green formula). Since high-resolution schemes require the computation of several quantities per mesh cell (e.g., slopes), the notion of “consistency” must be extended to this framework. A combination of consistency hypothesis with stability of the scheme leads to a suitable convergence theorem, generalizing the classical convergence theorem of Lax and Wendroff [52]. Finally, the limit functions are shown to be entropy solutions by using a notion of “Godunov compatibility”, which serves as a substitute to the entropy condition.

Inflation and dark matter from the low entropy hypothesis and modeling mechanism of modified gravity

Abstract The hypothesis of low entropy in the initial state of the Universe usually explains the observed entropy increase is in only one time direction: the thermodynamic arrow of time. The Hamiltonian formalism is commonly used in the context of general relativity. The set of Lagrange multipliers are introduced in the formalism, and they are corresponding to the Hamiltonian constraints which are written in terms of ‘weak equality’—the equality is satisfied if the constraints hold. Follow the low-entropy hypothesis, we postulate a modeling mechanism—a weak equality (of modeling) that holds only on the subspace of the theory space of physical models defined by some modeling constraints. By applying the modeling mechanism, we obtain a specific model of modified gravity under specific modeling conditions. We derive a novel equation of modeling from the mechanism, that describes how different gravitational models emerge. The solution of the modeling equation naturally turns out to be the model of R 2-gravity (with additional terms) if ordinary matter is negligible. We also found that this mechanism leads to two models: large-field inflation and wave-like dark matter (DM). Interestingly, the wave-like DM model is supported by the most recent observations of Einstein rings.

Revealing the influence of systemic risks in the development of enterprises on updating their investment position under entropy conditions

This study identifies the impact of systemic risks on the company's strategic development prospects through attracting investments and ensuring their insurance protection. The company's strategic development model predetermines the level of its investment activity at various stages of the life cycle. This is important because there is an urgent need for the Ukrainian economy to attract foreign investment for the post-war reconstruction of the country. But there are objective difficulties associated with the complication of actualizing the investment position of enterprises in the leading sectors of the economy, taking into account the challenges and threats caused by the military aggression of the Russian Federation. Conditions of entropy, which indicate unpredictability and variability in the business environment, expose enterprises to great risks. It was determined that the investment position of the business entity should correlate with the strategic model of its development and represent a balanced mechanism. This has made it possible to reasonably systematize the risk of investment activities and approaches to their management. Statistical analysis became the basis for evaluating the dynamics of direct and capital investments in the leading sectors of the Ukrainian economy. The results gave grounds for asserting a significant deterioration of the investment climate in Ukraine as a result of the war. The level of direct and capital investments is low. We focused attention on the possibility of flexible adjustment of strategic development plans to unforeseen risks. The proposed recommendations, unlike existing ones, consist of a combination of state and market levers to stimulate investments in the economy of Ukraine. Existing military risks restrain the investment activity of stakeholders. Therefore, the conditions for the practical implementation of the mechanism of distribution and reduction of risks are the formation of insurance protection of investments for investors

Toluene-Poisoning-Resistant High-Entropy Non-Noble Metal Anode for Direct One-Step Hydrogenation of Toluene to Methylcyclohexane.

The direct one-step hydrogenation of toluene to methylcyclohexane facilitated by a proton-exchange membrane water electrolyzer driven by renewable energy has garnered considerable attention for stable hydrogen storage and safe hydrogen transportation. However, a persistent challenge lies in the crossover of toluene from the cathode to the anode chamber, which deteriorates the anode and decreases its energy efficiency and lifetime. To address this challenge, the catalyst-poisoning mechanism is systematically investigated using IrO2 and high-entropic non-noble-metal alloys as anodes in acidic electrolytes saturated with toluene and toluene-oxidized derivatives, such as benzaldehyde, benzyl alcohol, and benzoic acid. Benzoic acid plays an important role in polymer-like carbon-film formation by blocking the catalytically active sites on the anode surface. Moreover, Nb and the highly entropic state on the surface of the multi-element alloy lower the adsorbing ability of toluene and prevent polymer-like carbon film formation. This study contributes to the design of catalyst-poisoning-resistant anodes for organic hydride technology, advanced fuel cells, and batteries.

A grave-to-cradle analysis of lithium-ion battery cathode materials using material and energy circularity indicators

The future demands for lithium-ion batteries required for powering the electrification transition in transportation and energy storage will lead to vast amounts of waste, demanding proper end-of-life strategies. As various recycling routes are continuously developed to address this issue, a significant challenge is the fair comparison of processes entailing different unit operations and transformation stages. Indeed, the choice of metallurgical or direct recycling routes results in diverse materials flows and energy demands. To allow a suitable comparison between technologies, this work presents a grave-to-cradle analysis of cathode materials (i.e., lithium cobalt oxide) considering three recycling processes representative of the most popular routes (i.e., pyrometallurgical, hydrometallurgical, and direct recycling). Unlike previously published works, a system-level analysis of both material recovery and energy preservation was carried out using statistical entropy and exergy analysis, respectively. Furthermore, comparison of processes using exentropy, a recently proposed circularity parameter combining both material recovery and energy preservation, was performed for the first time. The results highlight the need of a robust multidimensional analysis of processes to properly determine their suitability according to the needs of the circular economy. When materials and energy preservation were analyzed independently, two different routes were identified as optimal. The need of a robust multidimensional analysis of processes to properly account for the goals of the circular economy is thus highlighted. Exentropy analysis suggested that direct recycling provides the optimum alternative in terms of energy utilization for the recovery of materials.

Detecting Measurement-Induced Entanglement Transitions with Unitary Mirror Circuits.

Monitored random circuits, consisting of alternating layers of entangling two-qubit gates and projective single-qubit measurements applied to some fraction p of the qubits, have been a topic of recent interest. In particular, the resulting steady state exhibits a phase transition from highly correlated states with "volume-law" entanglement at p<p_{c} to localized states with "area-law" entanglement at p>p_{c}. It is hard to access this transition experimentally, as it cannot be seen at the ensemble level. Naively, to observe it one must repeat the experiment until the set of measurement results repeats itself, with likelihood that is exponentially small in the number of measurements. To overcome this issue, we present a hybrid quantum-classical algorithm which creates a matrix product state (MPS) based "unitary mirror" of the projected circuit. Polynomial-sized tensor networks can represent quantum states with area-law entanglement, and so the unitary mirror can well approximate the experimental state above p_{c} but fails exponentially below it. The breaking of this mirror can thus pinpoint the critical point. We outline the algorithm and how such results would be obtained. We present a bound on the maximum entanglement entropy of any given state that is well represented by an MPS, and from the bound suggest how the volume-law phase can be bounded. We consider whether the entanglement could similarly be bounded from below where the MPS fails. Finally, we present numerical results for small qubit numbers and for monitored circuits with random Clifford gates.

Computational Study of the Kinetics and Mechanisms of Gas-Phase Decomposition of N-Diacetamides Using Density Functional Theory.

In this research work, we examined the decomposition mechanisms of N-substituted diacetamides. We focused on the substituent effect on the nitrogen lone-pair electron delocalization, with electron-withdrawing and electron donor groups. DFT functionals used the following: B1LYP, B3PW91, CAMB3LYP, LC-BLYP, and X3LYP. Dispersion corrections (d3bj) with Becke-Johnson damping were applied when necessary to improve non-covalent interactions in the transition state. Pople basis sets with higher angular moments and def2-TZVP basis sets were also applied and were crucial for obtaining consistent thermodynamic parameters. The proposed mechanism involves a six-membered transition state with the extraction of an α hydrogen. Several conformers of N-diacetamides were used to account for the decrease in entropy in the transition state in the rate-determining state. All calculations, including natural bond orbital (NBO) analyses, were performed using the Gaussian16 computational package and its GaussView 6.0 visualizer, along with VMD and GNUPLOT software. The isosurfaces and IBSIs were calculated using MultiWFN and IGMPlot, respectively.

Understanding the Role of Entropy in Promoting Electrocatalytic CO2 Reduction

A global push towards increased sustainability requires technologies that enable the long-term storage of renewable electricity and the sustainable synthesis of chemicals. The electrochemical reduction of CO2 to fuels and chemicals represents a promising avenue to meet these goals. Yet, despite extensive research, many fundamental aspects of the interfacial interactions that enable this reaction remain unclear. One simple question that has not been addressed to date is the mechanism through which the applied potential controls the rate of CO2 reduction. To provide insight, we measured CO2 reduction activation energies on Ag electrodes in the presence of different cations. Building on our earlier work (J. Am. Chem. Soc. 2016, 138, 25, 7820–7823), where some of us demonstrated the important role of structural modifications to imidazolium cations in controlling the rate of CO2 reduction reactions, we expected that these structural modifications impact the reaction rate through changes to the activation energy. However, our findings revealed a much more fascinating picture of the impact of imidazolium cations on CO2 reduction rates.By measuring the activation energy in the presence of imidazolium cations with different structural features, we find that introducing 1-ethly-3-methylimidazolium (EMIM) results in an apparent activation energy of zero. Under these conditions, the applied potential modifies the reaction rate solely through changes to the pre-exponential factor of the Arrhenius equation.Based on literature on homogeneous catalysis, we suggest that our finding indicates that the rate of CO2 reduction in the presence of EMIM is entirely controlled by the formation entropy of the CO2 reduction transition state, with the potential likely influencing the rate by modifying the degree of ordering of imidazolium cations at the electrode surface. We further show that proton abstraction from EMIM forms a neutral compound, resulting in the elimination of the rate enhancement. Our results provide important new insight into the mechanism through which the applied potential controls the rate of electrocatalytic reactions and we expect them to be of broad importance to a better understanding of the connection between interface structure and electrocatalytic rates.

Mapping high entropy state spaces for novel material discovery

High-entropy alloys show promising properties for novel catalytic designs, but their vast potential configurations make them challenging to study computationally. Additionally, the traditional methods for data acquisition required to train neural networks on these broad systems can be inefficient. To address this, we propose an active learning methodology that integrates genetic algorithms with deep convolutional neural networks trained on Density Functional Theory calculations via a simple closed feedback loop. This approach streamlines data acquisition and the exploration of large configurational spaces simultaneously. We illustrate its effectiveness on high-entropy clusters of variable sizes and compositions, the vast state spaces of which are automatically explored and trained on, so as to generate and predict the stability of any cluster within the latent space given minimal computational requirements. Importantly, this method is adaptable for use in a variety of other systems of different sizes, chemical compositions, and stoichiometry.

ФИЗИКАНЫ ЖАНА АСТРОНОМИЯНЫ ОКУТУУДА ЖАНА ИЗИЛДӨӨДӨ МАТЕМАТИКАНЫН ОРДУ

This scientific article is devoted to the ways of using mathematics in teaching and researching the subjects of physics and astronomy. Newton's first polynomial was used in mathematical modeling of the emission of electron and hole color centers in solid state physics. Shannon's formula was used to determine information entropy, and the logarithmic function of Boltzmann's formula was used to determine statistical entropy. In astronomy, trigonometric functions and stereographic transformations are used to determine celestial coordinates and transform very large angles. This research paper will help students in their study of these disciplines. Particular attention is paid to the close connection between mathematics and astronomy and physics.

Impact of Quantum Non-Locality and Electronic Non-Ideality on the Shannon Entropy for Atomic States in Dense Plasma.

The influence of the collective and quantum effects on the Shannon information entropy for atomic states in dense nonideal plasma was investigated. The interaction potential, which takes into account the effect of quantum non-locality as well as electronic correlations, was used to solve the Schrödinger equation for the hydrogen atom. It is shown that taking into account ionic screening leads to an increase in entropy, while taking into account only electronic screening does not lead to significant changes.

Quality Fluctuation Abnormal Source Identification Based on Variable Weighted Reconstruction Analysis in Spinning Process

Due to the numerous and interconnected quality influencing parameters, the production process propagation and evolution of abnormal factors are complex, which can affect the stability of quality characteristics from multiple perspectives. This paper addresses the problem of identifying the quality fluctuations sources and proposes a variable-weighted reconstruction analysis-based method for identifying abnormal sources of quality fluctuations in the spinning process. The method monitors the degree of quality fluctuations by constructing information entropy statistics and reconstructs the weighted parameters of abnormal quality processes. On this basis, abnormal contribution ranking is performed based on the degree of change in quality characteristics before and after weight reconstruction, which achieves the identification of the abnormal source. The proposed method is validated using a spinning process dataset. It reveals that the method could accurately identify the quality fluctuation abnormal source, which indicates its practicability and feasibility and will provide a theoretical basis for the quality stability control.