Evolution Of Entropy Research Articles

4 Boyutlu Modelde Spinör Tipi İnstanton Çözümlerinin Dalgacık Entropisinin İncelenmesi

In recent years, many methods have been proposed in various fields to investigate the properties of orbits of nonlinear dynamical systems. In this study, the characteristics of the orbits of spinor-type instanton solutions in the four-dimensional Gursey model via Heisenberg ansatz is investigated. The orbits of spinor-type instanton solutions are analyzed by Shannon wavelet entropy (WE) method. In order to analyze the regular or irregular states of the orbits of spinor-type instanton solutions, WE spectrum and WE in phase space are studied. It is observed that spinor-type instanton solutions have regular orbits around the fixed point and irregular orbits for other points. According to this study, WE can be used to observe the entropy evolution of nonlinear dynamical systems in phase space.

Research on the Nonlinear Random Matrix Model for Urban Information Model and Modern Urban Governance

In this paper, a nonlinear stochastic matrix approach is used to conduct an in-depth study and analysis of modern urban governance, and an urban information model is designed for practical application based on it. Random matrix theory can calculate and give the average result of all interactions contained in a complex system. By comparing the different characteristics of statistical properties of real systems and random matrices, the special nonrandom properties of real systems are deduced. The dissipative structure theory of open complex systems, the evolution of network entropy describing the robustness of complex networks, can explain the empirical results of random matrix theory from the point of view of system evolution; through the open development of fair data and prevention tools to achieve algorithm correction, promote the design optimization of intelligent models, intelligent platforms, and intelligent programs; and commit to the benign development of technology. At the institutional level, it is necessary to keep the smart city construction synchronized with the rule of law construction, with a two-pronged approach of policy incentives and legal constraints, in addition to the overall promotion of government transformation and pluralistic governance patterns. It exceeds the carrying capacity and adaptability of social systems and institutions. In fact, the productive forces with science and technology as the core are the most active forces in social change and development. The urban information model is a technical and conceptual change triggered by the wave of information in the field of urban planning and construction and urban management, which takes the 3D model as a carrier to realize digital information application and unification in the whole life cycle of territorial spatial planning, urban design, and engineering and construction projects through the simulation of spatial planning and urban design spatial elements as well as the entry, management, and application of engineering and construction project information. Digital technology is applied in the whole life cycle of land spatial planning, urban design, and engineering projects to achieve fine governance and efficient management of urban planning.

A statistical analysis of COVID-19 pandemic based on the temporal evolution of entropy in different countries

Objective: Currently the Covid-19 pandemic is studied with great expectations by several epidemiological models with the aim of predicting the future behaviour of the pandemic. Determining the level of disorder in the pandemic can give us insight into the societal reactions to the pandemic the socio-economic structures and health systems in different countries. Methods: We perform a statistical analysis of Covid-19 pandemic using an entropy measure. For this, the Boltzmann-Gibbs-Shannon (BGS) entropy method is applied to the daily case data and the predictability in the covid-19 pandemic is discussed based on its entropic behaviour. The BGS entropy of the time evolution of daily cases in weekly groups from the beginning of the pandemic to 29 August 2021 in the UK, Germany, France, Italy, and Spain, Turkey, Russia and Iran are calculated and the given countries are classified by the predictability of the spread of the pandemic. Results: There is a clear difference in the predictability of the pandemic between the European countries and Turkey, Russia, and Iran. It is also observed that the vaccination programs and the Covid-19 variants of concerns; 20I/501Y.V1, 20H/501.V2, 21A/S:478K and 20J/501Y.V3 have effected the predictability of the pandemic in given countries are observed. Conclusion: The BGS entropy-based approach to determine the disorder in the time evolution of daily cases of the Covid-19 pandemic is effective and the results can be beneficial for comparison of the country classifications generated by the epidemiological models of this pandemic system.

Optimal control for state preparation in two-qubit open quantum systems driven by coherent and incoherent controls via GRAPE approach

In this work, we consider a model of two qubits driven by coherent and incoherent time-dependent controls. The dynamics of the system is governed by a Gorini–Kossakowski–Sudarshan–Lindblad master equation, where coherent control enters into the Hamiltonian and incoherent control enters into both the Hamiltonian (via Lamb shift) and the dissipative superoperator. We consider two physically different classes of interaction with coherent control and study the optimal control problem of state preparation formulated as minimization of the Hilbert–Schmidt distance’s square between the final density matrix and a given target density matrix at some fixed target time. Taking into account that incoherent control by its physical meaning is a non-negative function of time, we derive an analytical expression for the gradient of the objective and develop optimization approaches based on adaptation for this problem of GRadient Ascent Pulse Engineering (GRAPE). We study evolution of the von Neumann entropy, purity, and one-qubit reduced density matrices under optimized controls and observe a significantly different behavior of GRAPE optimization for the two classes of interaction with coherent control in the Hamiltonian.

Generalized Entropy Production in Collisionless Plasma Flows and Turbulence

A new general theoretical framework for entropy production helps demonstrate, in simulations, the production of entropy in collisionless plasmas, whose entropy evolution has long been an outstanding problem.

Holographic β Function in de Sitter Space

The scale invariance of the universe is slightly broken by slow roll parameters. It is likely the slow roll is dual to the random walk. We investigate the distribution function of the conformal zeromode. We identify de Sitter entropy $S_{dS}$ with the distribution entropy of the conformal zeromode $\rho(\omega)$. We have collected convincing support on our postulate. The semiclassical evidence is that the both are given by the gravitational coupling $1/g=\log N/2$ where $g=G_NH^2/\pi$ and $N$ is the e-folding number. We show the renormalized distribution function obeys gravitational Fokker-Planck equation (GFP) and Langevin equations . Under the Gaussian approximation, they boil down to a simple first order partial differential equation. The identical equation is derived by the thermodynamic arguments in the inflationary space-time. GFP determines the evolution of de Sitter entropy of the universe. It coincides with $\beta$ function of $g$. We find two types of the solutions of GFP:(1) UV complete spacetime and (2) inflationary spacetime with power potentials. The maximum entropy principle favors the scenario: (a) born small $\epsilon$ and (b) grow large by inflation. We like to convey the emerging notion of de Sitter duality. The inflationary universe: (bulk/geometrical) is dual to the stochastic space-time on the boundary (cosmological horizon ) as the both are the solutions of GFP.

Second law of information dynamics

One of the most powerful laws in physics is the second law of thermodynamics, which states that the entropy of any system remains constant or increases over time. In fact, the second law is applicable to the evolution of the entire universe and Clausius stated, “The entropy of the universe tends to a maximum.” Here, we examine the time evolution of information systems, defined as physical systems containing information states within Shannon’s information theory framework. Our observations allow the introduction of the second law of information dynamics (infodynamics). Using two different information systems, digital data storage and a biological RNA genome, we demonstrate that the second law of infodynamics requires the information entropy to remain constant or to decrease over time. This is exactly the opposite to the evolution of the physical entropy, as dictated by the second law of thermodynamics. The surprising result obtained here has massive implications for future developments in genomic research, evolutionary biology, computing, big data, physics, and cosmology.

Entanglement entropy and flow in two-dimensional QCD: Parton and string duality

We discuss quantum entanglement between fast and slow degrees of freedom, in a two dimensional (2D) large $N_c$ gauge theory with Dirac quarks, quantized on the light front. Using the 't Hooft wave functions, we construct the reduced density matrix for an interval in the momentum fraction $x$-space, and calculate its von Neumann entropy in terms of structure functions, that are measured by DIS on mesons (hadrons in general). We found that the entropy is bounded by an area law with logarithmic divergences, proportional to the rapidity of the meson. The evolution of the entanglement entropy with rapidity, is fixed by the cumulative singlet PDF, and bounded from above by a Kolmogorov-Sinai entropy of 1. At low-$x$, the entanglement exhibits an asymptotic expansion, similar to the forward meson-meson scattering amplitude in the Regge limit. The evolution of the entanglement entropy in parton-$x$ per unit rapidity, measures the meson singlet PDF. The re-summed entanglement entropy along the single meson Regge trajectory, is string-like. We suggest that its extension to multi-meson states, models DIS scattering on a large 2D $^\prime$nucleus$^\prime$. The result, is a large rate of change of the entanglement entropy with rapidity, that matches the current Bekenstein-Bremermann bound for maximum quantum information flow. This mechanism may be at the origin of the large entropy deposition and rapid thermalization, reported in current heavy ion colliders, and may extend to future electron-ion colliders.

Fractional memetic computing paradigm for reactive power management involving wind-load chaos and uncertainties

Optimal reactive power dispatch (ORPD) with integration of renewable energy resources has a growing interest in research community due to its utmost requirements during the operation, planning and design of the modern electrical power networks. The objective of ORPD is to improve the performance of power network by means of reducing the losses in transmission line, improving the voltage profile, and decreasing the overall cost of operation through optimal tuning of the operational variables such as tap position of transformers, generator output voltages and capacitor banks. However, the nonlinear, non-stationary and complex nature of power network, presence of load uncertainties, and dynamic behavior of wind generation introduces a complex optimization task which cannot be readily solved in an efficient manner. In this research work, a new fractional memetic computing paradigm, i.e., the fractional particle swarm optimization gravitational search algorithm with entropy evolution (FPSOGSA-EE), is designed to solve the ORPD problems in power system adopting wind power plants (WPPs) and load uncertainties. The proposed optimization framework FPSOGSA-EE integrates the concept of fractional calculus and Shannon entropy to strengthen the optimization characteristics of canonical algorithm. The exhaustive experimentation endorse the efficacy of FPSOGSA-EE by providing minimum gauge of fitness evaluation function, namely, the line loss and voltage deviation index minimization, in IEEE 30 and 57 bus networks. The stability, consistency and reliability of proposed FPSOGSA-EE is ascertained through statistical interpretations by means of boxplots, probability measures for cumulative distribution function, and histogram illustrations.

Emergence of space and expansion of Universe

According to the principle of emergence, the expansion of the Universe can be explained as the emergence of space with the progress of cosmic time. We have analytically solved the equation of emergence proposed by Padmanabhan by assuming the Komar energy density ρ + 3P as a function of the Hubble parameter. The resulting model describes the evolution of the Universe, which proceeds towards a final de Sitter state. Model parameters have been extracted using the cosmological observational data. Further, the horizon entropy evolution of the model has been studied. The model predicts a Universe having a transition from a prior decelerated epoch to a late accelerated epoch and reasonably predicts the cosmological constant.

Performance analysis of relaxation Runge–Kutta methods

Recently, global and local relaxation Runge–Kutta methods have been developed for guaranteeing the conservation, dissipation, or other solution properties for general convex functionals whose dynamics are crucial for an ordinary differential equation solution. These novel time integration procedures have an application in a wide range of problems that require dynamics-consistent and stable numerical methods. The application of a relaxation scheme involves solving scalar nonlinear algebraic equations to find the relaxation parameter. Even though root-finding may seem to be a problem technically straightforward and computationally insignificant, we address the problem at scale as we solve full-scale industrial problems on a CPU-powered supercomputer and show its cost to be considerable. In particular, we apply the relaxation schemes in the context of the compressible Navier–Stokes equations and use them to enforce the correct entropy evolution. We use seven different algorithms to solve for the global and local relaxation parameters and analyze their strong scalability. As a result of this analysis, within the global relaxation scheme, we recommend using Brent’s method for problems with a low polynomial degree and of small sizes for the global relaxation scheme, while secant proves to be the best choice for higher polynomial degree solutions and large problem sizes. For the local relaxation scheme, we recommend secant. Further, we compare the schemes’ performance using their most efficient implementations, where we look at their effect on the timestep size, overhead, and weak scalability. We show the global relaxation scheme to be always more expensive than the local approach—typically 1.1–1.5 times the cost. At the same time, we highlight scenarios where the global relaxation scheme might underperform due to its increased communication requirements. Finally, we present an analysis that sets expectations on the computational overhead anticipated based on the system properties.

Complexity in a moving mirror model

In a two-dimensional conformal field theory with a moving mirror, known as a moving mirror model, the time evolution of the entanglement entropy shows a Page like curve. This implies that the moving mirror model is useful to understand the island formula. In this paper, we study the time evolution of the subregion CV complexity in the moving mirror model for a better understanding of the island formula of the complexity. In contrast to the entanglement entropy, the subregion CV complexity shows a peculiar behaviour. We discuss this behaviour in more detail.

Coriolis coupling in a Hénon–Heiles system

We study the impact of a Coriolis term in the dynamics of a perturbed Hénon–Heiles Hamiltonian. The strength of the Coriolis coupling is measured by a frequency ω that regulates two different regimes. If (in scaled units) ω1, the minimum becomes a dynamically stable maximum, and there appears an open region of stable motion around that maximum. We restrict our study to ω∈[0,1) because we find richer dynamics in that interval. Poincaré surfaces of section are used to show how the strength of the Coriolis coupling controls the size of the trapping area. While, for ω=0, most of the orbits escape, for ω≈1 most of the orbits remain trapped. The transition from one situation to the other one reveals complex resonant structures giving rise to a chaotic sticky region of long living orbits. The study of the escape basins reveals that they evolve from a complex structure, with fractal boundaries, to basins with smooth boundaries. Explicit computation of the evolution of the basin entropy confirms this fact. The escape probability as a function of ω is also calculated. Both the evolution of the escape probability and the entropy are not monotonic and exhibit intricate and complex dynamics for intermediate values of ω.

Exact Time Evolution of Genuine Multipartite Correlations for N-Qubit Systems in a Common Thermal Reservoir

We investigate the dynamical evolution of genuine multipartite correlations for N-qubits in a common reservoir considering a non-dissipative qubits-reservoir model. We derive an exact expression for the time-evolved density matrix by modeling the reservoir as a set of infinite harmonic oscillators with a bilinear form of interaction Hamiltonian. Interestingly, we find that the choice of two-level systems corresponding to an initially correlated multipartite state plays a significant role in potential robustness against environmental decoherence. In particular, the generalized W-class Werner state shows robustness against the decoherence for an equivalent set of qubits, whereas a certain generalized GHZ-class Werner state shows robustness for inequivalent sets of qubits. It is shown that the genuine multipartite concurrence (GMC), a measure of multipartite entanglement of an initially correlated multipartite state, experiences an irreversible decay of correlations in the presence of a thermal reservoir. For the GHZ-class Werner state, the region of mixing parameters for which there exists GMC, shrinks with time and with increase in the temperature of the thermal reservoir. Furthermore, we study the dynamical evolution of the relative entropy of coherence and von-Neumann entropy for the W-class Werner state.

Information Bottleneck in Deep Learning - A Semiotic Approach


 
 
 The information bottleneck principle was recently proposed as a theory meant to explain some of the training dynamics of deep neural architectures. Via information plane analysis, patterns start to emerge in this framework, where two phases can be distinguished: fitting and compression. We take a step further and study the behaviour of the spatial entropy characterizing the layers of convolutional neural networks (CNNs), in relation to the information bottleneck theory. We observe pattern formations which resemble the information bottleneck fitting and compression phases. From the perspective of semiotics, also known as the study of signs and sign-using behavior, the saliency maps of CNN’s layers exhibit aggregations: signs are aggregated into supersigns and this process is called semiotic superization. Superization can be characterized by a decrease of entropy and interpreted as information concentration. We discuss the information bottleneck principle from the perspective of semiotic superization and discover very interesting analogies related to the informational adaptation of the model. In a practical application, we introduce a modification of the CNN training process: we progressively freeze the layers with small entropy variation of their saliency map representation. Such layers can be stopped earlier from training without a significant impact on the performance (the accuracy) of the network, connecting the entropy evolution through time with the training dynamics of a network.
 
 

Unusual wave-packet spreading and entanglement dynamics in non-Hermitian disordered many-body systems

Non-Hermiticity and dephasing, collaborating in an unusual wave packet dynamics, realizes unconventional entanglement evolution in a disordered, interacting and asymmetric (non-reciprocal) quantum medium. Taking the Hatano-Nelson model as a concrete example, we first consider how wave packet spreads in a non-Hermitian disordered system for demonstraing that it is very different from the Hermitian case. Interestingly, a cascade like wave packet spreading as in the Hermitian case is suppressed in the clean limit and at weak disorder, while it revives in the vicinity of the localization-delocalization transition. Based on this observation, we then analyze how the entanglement entropy of the system evolves in the interacting non-Hermitian model, revealing its non-monotonic evolution in time. We clarify the different roles of dephasing in the time evolution of entanglement entropy in Hermitian and non-Hermitian systems, and show that the many-body dynamics is governed by a principle different from the Hermitian case. The size dependence of the results suggests with the increase of disorder, a unusual area-volume-area law crossover of the maximal entanglement entropy. To analyze the effects of disorder on a firm basis, using the Hermitian limit as a benchmark, we employ a quasi-periodic disorder (Aubry-Andr\'{e} model) in the analyses.

Disorder-driven phase transitions in bosonic fractional quantum Hall liquids

We investigate the disorder-driven phase transitions in bosonic fractional quantum Hall liquids at filling factors $f=1/2$ and $f=1$ in the lowest Landau level. We use the evolution of ground-state entanglement entropy, fidelity susceptibility, and Hall conductance with increasing disorder strength to identify the underlying phase transitions. The critical disorder strengths obtained from these different quantities are consistent with each other, validating the reliability of our numerical calculations based on exact diagonalization. At $f=1/2$, we observe a clear transition from the bosonic Laughlin state to a trivial insulating phase. At $f=1$, we identify a direct phase transition from the non-Abelian bosonic Moore-Read state to a trivial insulating phase, although some signs of a disorder-induced intermediate fractional quantum Hall phase were recently reported for the $f=5/2$ fermionic cousin.

Photon statistics and non-local properties of a two-qubit-field system in the excited negative binomial distribution

In this paper, a quantum scheme for a two-qubit system (2QS) and field initially prepared in the excited negative binomial distribution is presented. The field photon statistics is detected from the evolution of the Mandel parameter, while the evolution of von Neumann entropy detects the nonlocal correlation between the 2QS and radiation field. The concurrence is used to detect the qubit-qubit entanglement during the time evolution. The dynamical properties of single-qubit and two-qubit quantum Fisher information are investigated. We visualize the number of photon excitations on the field in negative binomial states with influence of photon success probability. A connection is provided between the dynamical behaviors of these statistical quantities. We have found that the proposed quantities are strongly influenced by the number of excited photons of the field in negative binomial states and photon success probability.

Effect of temperature on corrosion inhibition by ethanolic extract of Eriobotrya Japonica seeds in chloride medium 1M

This work investigated the effect of temperature on corrosion of C38 steel in a hydrochloric medium (1M) in the absence and presence of the ethanolic extract from Eriobotrya Japonica (ERJ) seeds treated by maceration. For a better understanding of the corrosion process, electrochemical impedance spectroscopy (EIS) and potentiodynamic polarization techniques had applied by increasing the temperature from 303.15 K to 333.15 K. Moreover, studying adsorption isotherms and determining thermodynamic parameters to understand the mechanism adopted in the adsorption of ERJ molecules on the metal surface. The results reveal that the inhibition efficiency increases with higher inhibitor concentration and decreases slightly with increasing temperature. Thus, the Langmuir model is the best model to fit the data obtained, and the adsorption follows a spontaneous physisorption process. According to the evolution of enthalpy, entropy, and activation energy, the inhibition capacity decreases is associated with a slow endothermic dissolution due to forming an active complex on the surface of C38.

Dialectical Behavior Group Therapy for Adolescents and Parents: Analysis of Answer Entropy

Introduction: The work’s purpose is to study the group behavior of the members of six therapeutic groups, two closed and four slow-open, involved in a Dialectical Behavior Therapy (DBT) class. We studied three groups of teenagers and three of their parents or legal guardians. We confronted the groups’ responses to an “absurd questionnaire” submitted during the training, and we concentrated on the entropy of the response. Methods: The research method consists of a questionnaire administered to training attendees. Participants chose one picture in each one of 50 couples (“absurd questionnaire”). In this work, we could propose a questionnaire to each trainee before the first meeting of the groups. We studied the longitudinal evolution of entropy, and we also compared the six groups according to their first picture choices and their evolution, the changes in the choices, the number of changes (flux), and the divergence or convergence toward the initial answer (focus). We have also analyzed the frequency of entropy variation via the Fourier transform. Results: We find the maximum statistical difference between parents’ and adolescents’ closed groups. The entropy trend is steeper in the adolescent closed group. The entropy evolution depends more on the age group (parents or adolescents) in closed and slow-open groups than on the setting. We found an increase in entropy from the beginning to the end of the training in all the groups. Conclusions: The clear outcome of this study is the augmentation in entropy in all the groups regardless of the settings (closed or slow-open) and possibly a similar entropy’s dominant oscillation frequency, that is, the number of complete cycles in the training interval, regardless of the type of group and the training duration.