Entropic Characteristics Research Articles

Quantum entropic exchange at avoided crossings due to laser–atom interaction

In the present study, we detail the entropic characteristics of a dressed atom, wherein the atom undergoes an interaction with a monochromatic laser beam. Our investigation of the laser–atom interplay employs a well-established non-perturbative quasi-energy methodology, allowing us to discern the dressed wavefunctions and quasi-energies of the laser-dressed atom. Utilizing these dressed wavefunctions as a foundation, we systematically examine various entropic measures, observing their behaviour for laser frequency and intensity. The selection of levels within the system adheres to the criteria dictated by the selection rules governing transitions between these levels. Our exploration focuses on the interplay between Shannon entropy and other entropic metrics, with their fluctuations intricately tied to the phenomenon of avoided crossings. As the laser amplitude intensifies, the AC Stark effect takes centre stage, exerting influence over the sharp or smooth variations in Shannon entropy at these avoided crossings. Furthermore, we delineate the correlation between the number of levels considered and the identification of avoided crossings. Our present analysis sheds light on the intricate dynamics in the dressed atom system, enhancing our understanding of the interplay between laser-induced dressing and entropic measures.

Using Yield and Entropy-Based Characteristics for Circular Economy

Environmental impacts of the extant linear carbon economy and aspects of conservation of resources demand a transformation to a circular carbon economy (CCE). In view of this transformation, carbon-containing plastic products should be reused and recycled to prevent or minimize the release of their carbon content into the environment. Different plastic waste feedstock recycling strategies are applicable, with different degrees of feedstock destruction, depending on the degree of degradation and contamination of the intended recycle fractions. The evaluation of the effectiveness of recycling processes by substance and carbon-based yield and entropic characteristics could be a part of the overall evaluation strategy for recycling processes. Possible principles and base equations of such substance and carbon-based yield and entropic characteristics, extracted from the literature and adapted, are delineated in this article. Substance-based characteristics could be applied for physical recycling processes in which the aspired recovery substances remain preserved and are physically separated. A resort to carbon-based characteristics could be practiced for recycling and combustion processes, in which the feedstock is chemically destroyed, and new substances are possibly synthesized. Stylized process examples depict the way of a joint usage of yield and entropic characteristics.

The Question of Studying Information Entropy in Poetic Texts

One of the approaches to quantitative text analysis is to represent a given text in the form of a time series, which can be followed by an information entropy study for different text representations, such as “symbolic entropy”, “phonetic entropy” and “emotional entropy” of various orders. Studying authors’ styles based on such entropic characteristics of their works seems to be a promising area in the field of information analysis. In this work, the calculations of entropy values of the first, second and third order for the corpus of poems by A.S. Pushkin and other poets from the Golden Age of Russian Poetry were carried out. The values of “symbolic entropy”, “phonetic entropy” and “emotional entropy” and their mathematical expectations and variances were calculated for given corpora using the software application that automatically extracts statistical information, which is potentially applicable to tasks that identify features of the author’s style. The statistical data extracted could become the basis of the stylometric classification of authors by entropy characteristics.

Hurst entropy profiles for Beta Low and Beta High EEG sub-bands Part I: Intragroup comparison.

The non-linear exploration of the entropic structure of the information contained in an EEG allows access to a new source of data that characterizes, in a more global way, the functioning of the brain as a whole. On the understanding that the brain is a hyper-complex system, describing it only through a linear statistical approach, mainly based on the comparison of differences in the magnitude of the power of the electroencephalographic signal between comparable conditions, leaves incomplete the part of the brain phenomenon that obeys non-linear laws. The present work explores the possibility of characterizing the entropic structure of a human brain, through the construction of order/chaos balance profiles. We proceeded to study the entropic content of the EEG signal, by estimating the Hurst exponent in segments of different sizes, for a set of data from 14 EEG electrodes (Emotiv Epoc Research Edition), taken in basal resting conditions, during 3-5 minutes with eyes closed. The EEG recordings of thirteen subjects (N=13) were studied for the low beta (13-21Hz) and high beta (22-30Hz) sub-bands, in four time-processing windows: 125ms, 250ms, 500ms, and 1s. In addition to obtaining the traditional Hurst estimator, the behavior of two derivatives of the Hurst exponent: the moving-Hurst (muHurst), and the mHurst, an estimator interpreted as a global entropic trend of the time series, were also evaluated. The results showed a clear differentiation between the entropic profiles obtained for low beta and high beta, for all individuals, as well as a different entropic structure of both sub-bands, when comparing Hurst exponents and their derivatives with different time processing windows. At the 1s scale (128 EEG frames), the average entropic content of the time series (muHurst) is relatively higher than the entropic load contained in the mid-term estimation of the whole signal (H(trad)). At the same time, estimates of mHurst, a derivative that assesses the overall entropic trend of the signal, indicated mostly lower entropic (more organized) content than estimates at shorter timescales. Our nonlinear exploration of the entropic structure of the brain revealed a wealth of details that can be used to complement the traditional characterization of the brain that linear approaches have provided so far. Our procedure allowed us to discern substantive differences between the entropic characteristics of the low beta and high beta EEG sub-bands. As well as individual differences within the group, potential substrates for the search of neural markers of psychological, pharmacological, or clinical utility.

Effect of the Number of Nozzles of Swirl Flow Generator Utilized in Flat Plate Solar Collector: An Entropic Analysis

The numerical model of the pipes of a flat plate solar collector (FPSC) with several nozzles has been investigated in the present study. Indeed, the effect of the number of nozzles of the swirl generator on the entropic characteristics has been evaluated. The nozzles were applied for improving the performance of FPSC. For evaluating the proposed system based on the entropy concept, the effect of injection angle and mass flow rate has been considered. The selected injection angles were 30°, 45°, 60°, and 90°. Also, the total mass flow rates entered from all of the nozzles were 0.2 kg/s, 1 kg/s, and 2 kg/s. The effect of said variables on frictional and thermal entropy generations was analyzed; then, the overall energetic-entropic performance of the system was predicted using several dimensionless parameters including NE, NS, Nu ∗ , and heat transfer improvement (HTI). Moreover, Witte-Shamsundar efficiency ( η W − S ) was applied to pinpoint the efficiency of the system. The highest value of HTI and η W − S was 1.7 and 0.9 that achieved by “single-nozzle; A90-D50-N12.5-M0.2” and “quad-nozzle; A30-D50-N12.5-M2,” respectively.

On Quantum States with a Finite-Dimensional Approximation Property

We consider a class (convex set) of quantum states containing all finite rank states and infinite rank states with the sufficient rate of decreasing of eigenvalues (in particular, all Gaussian states). Quantum states from this class are characterized by the property (called the FA-property) that allows to obtain several results concerning finite-dimensional approximation of basic entropic and information characteristics of quantum systems and channels. We obtain a simple sufficient condition of the FA-property. We show that this property implies finiteness of the von Neumann entropy, but leave unsolved the question concerning the converse implication. We obtain uniform approximation results for characteristics depending on a pair (channel, input state) and for characteristics depending on a pair (channel, input ensemble). We establish the uniform continuity of the above characteristics as functions of a channel w.r.t. the strong convergence provided that the FA-property holds either for the input state or for the average state of input ensemble.

Mechanical analysis of non-Newtonian nanofluid past a thin needle with dipole effect and entropic characteristics

The study concerns with the mechanical characteristics of heat and mass transfer flow of a second grade nanofluid as well as gyrotatic microorganism motion past a thin needle with dipole effect, entropy generation, thermal radiation, Arrhenius activation energy and binar chemical reaction. The governing equations and boundary conditions are simplified by the use of suitable similarity transformations. Homotopy analysis method is implemented to obtain the series solution of non-linear ordinary differential equations. Physical behaviors of heat and mass transfer flow with gyrotatic microorganisms and entropy generation are investigated through the embedded parameters. The nanofluid velocity is enhanced for higher values of the ferromagnetic parameter, local Grashof number, bioconvection Rayleigh number and radiation parameter. The Reynolds number, radiation parameter and Eckert number decrease the nanofluid temperature. The entropy generation is increased with the enhancement of radiation parameter, Eckert number, Lewis number, temperature difference parameter, dimensionless constant parameter, Curie temperature, Prandtl number and concentration difference parameter.

Entropic analysis of a double helical tube heat exchanger including circular depressions on both inner and outer tube

In this research, entropic analysis of a double helical tube heat exchanger including circular depressions on both inner tube and outer tube is provided. Experimentally validated 3D numerical simulation is employed to reach the aim of this study. Entropic characteristics of four cases are investigated and reported. In case “a” both inner tube and outer tube are smooth. In case “b”, circular depressions are created on only inner tube while in case “c” both tubes contain circular depression. Case “d” is the same as case “c” while the depression arrangement is different from case “c”. Dimensionless entropy generation and dimensionless Nu number are used to evaluate the proposed designs based on the first and second laws of thermodynamics. Moreover, heat transfer improvement (HTI) factor is adopted to consider the impacts of said two parameters simultaneously. Results demonstrate that, although creating circular depressions on both tubes significantly improves the heat transfer characteristics of the heat exchanger, it increases the entropy generation level of heat exchanger as well. Case “d” in which the location of any circular depression of the outer tube is placed between any two continuous depressions of the inner tube, gives the highest thermal performance and also entropy generation.

A Scale-Invariant Generalization of the Rényi Entropy, Associated Divergences and Their Optimizations Under Tsallis’ Nonextensive Framework

Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization of the entropy and the minimization of the cross entropy or relative entropy (divergence), are essential for general logical inference in our physical world. In this paper, we discuss a two parameter generalization of the popular R\'{e}nyi entropy and associated optimization problems. We derive the desired entropic characteristics of the new generalized entropy measure including its positivity, expandability, extensivity and generalized (sub-)additivity. More importantly, when considered over the class of sub-probabilities, our new family turns out to be scale-invariant. We also propose the corresponding cross entropy and relative entropy measures and discuss their geometric properties including generalized Pythagorean results over $\beta$-convex sets. The maximization of the new entropy and the minimization of the corresponding cross or relative entropy measures are carried out explicitly under the non-extensive (`third-choice') constraints given by the Tsallis' normalized $q$ expectations which also correspond to the $\beta$-linear family of probability distributions. Important properties of the associated forward and reverse projection rules are discussed along with their existence and uniqueness. In this context, we have come up with, for the first time, a class of entropy measures -- a subfamily of our two-parameter generalization -- that leads to the classical (extensive) exponential family of MaxEnt distributions under the non-extensive constraints. Other members of the new entropy family, however, lead to the power-law type generalized $q$-exponential MaxEnt distributions which is in conformity with Tsallis' nonextensive theory.

Magnetic-induced nanoparticles and rotary tubes for energetic and exergetic performance improvement of compact heat exchangers

In the present study, the effects of rotary tubes and magnetic-induced nanofluid on heat transfer characteristics of a compact heat exchanger are individually investigated. Two-phase Eulerian model is employed to predict the hydrothermal and entropic characteristics of Fe3O4/water ferrofluid in the heat exchanger. Results indicate that utilizing each rotary tubes and magnetic field method can improve the energy and exergy efficiencies of the compact heat exchanger under specific circumstances by forming different types of secondary flow. It is found that employing each method individually can increase the maximum heat transfer rate by more than 60%. In comparison with methods like passive vortex and swirl generators, subtle pressure drop and entropy generation is observed in the new proposed methods since no additional obstacles were employed. Results also reveal that 12.5% of the possible maximum energy can be regenerated along with a 3.5% increase in the exergy efficiency of the heat exchanger at low Reynolds numbers by employing each method.

Schrödinger Equation for Energy Levels as a Linear Equation for Probability Distributions Identified with Quantum States

In this paper, we show that the energy spectrum of a qudit system (spin-j, N-level atom) with Hamiltonian N×N matrix H is determined by the equation for eigenvalues of the N2×N2 matrix ℋ and its eigenvectors | p⟩ with components, which are probability distributions identified with quantum states in the probability representation of quantum mechanics. We derive this equation based on the conventional Schrodinger equation for the state vector | ψ⟩. We discuss the example of qubit in detail and study new entropic characteristics of the energy levels.

COVID-19 ENTROPIC CHARACTERISTICS

It is demonstrated that according to the first law of thermodynamics the equality of entropic and negentropic components is the condition of resonance stationary state of systems. In the systems in which the interaction proceeds along the potential gradient (positive work), the resultant potential energy is found based on the principle of adding reciprocals of corresponding values of subsystems. This is the corpuscular process, in which entropy can serve as the theoretical concept. In the systems in which the interactions proceed against the potential gradient (negative work) the algebraic addition of their masses, as well as the corresponding energies of subsystems is performed. This is the wave process, in which negentropy can serve as the theoretical concept. The resonance stationary state of the systems is fulfilled under the condition of equality of degrees of their corpuscular and wave interactions. The entropy products in stationary state are completely compensated by the negentropy flow. Mathematically and graphically (by nomograms) the stationary state in microsystems is found by the following equation containing the tangent of the geodesic angel. The geodesic angle numerically defines the ratio of two legs of the right triangle whose values characterize energy dependencies through axial and circumferential stresses in the system with corpuscular-wave processes. This condition corresponds to the most optimal technological options and is widely present in nature, as well as in fractal systems. The initial nomograms of entropic and negentropic characteristics for many processes and phenomena in nature, engineering and physical chemistry are given. The entopic technique for forming fractal systems is presented. The coronavirus scenario in Russia is analyzed. The accuracy of forecast regarding the maximum number of diseases at the given moment and plateau duration is 96.5 % and 98.5%, respectively.

Advanced Alicki–Fannes–Winter method for energy-constrained quantum systems and its use

We describe an universal method for quantitative continuity analysis of entropic characteristics of energy-constrained quantum systems and channels. It gives asymptotically tight continuity bounds for basic characteristics of quantum systems of wide class (including multi-mode quantum oscillators) and channels between such systems under the energy constraint. The main application of the proposed method is the advanced version of the uniform finite-dimensional approximation theorem for basic capacities of energy-constrained quantum channels.

Quantum‐Memory‐Assisted Entropic Uncertainty Relations

AbstractUncertainty relations take a crucial and fundamental part in the frame of quantum theory, and are bringing on many marvelous applications in the emerging field of quantum information sciences. Especially, as entropy is imposed into the uncertainty principle, entropy‐based uncertainty relations lead to a number of applications including quantum key distribution, entanglement witness, quantum steering, quantum metrology, and quantum teleportation. Herein, the history of the development of the uncertainty relations is discussed, especially focusing on the recent progress with regard to quantum‐memory‐assisted entropic uncertainty relations and dynamical characteristics of the measured uncertainty in some explicit physical systems. The aims are to help deepen the understanding of entropic uncertainty relations and prompt further explorations for versatile applications of the relations on achieving practical quantum tasks.

Experimental investigation on the thermal and entropic behavior of a vertical helical tube with none-boiling upward air-water two-phase flow

Helical tubes have great compact structure, two-phase flow stability and well thermal performance. The increment of applications which use two-phase flow in helical tubes, necessitates the investigation on thermal and entropic characteristics of two-phase flow in helically coiled tubes. The present study provides experimental results of heat transfer characteristics of upward air-water none-boiling two-phase flow in a vertical helically coiled tube. The helical tube was put under constant heat flux. The inlet, outlet, wall and ambient temperature of helical tube were measured for calculating the heat transfer coefficient and entropy generation. The water superficial Dean number (Desl) was between 1000 and 4800. Also, the gas (air) superficial Dean number (Desg) was between 45 and 235. The VF (volume fraction) fraction was between 0.11 and 0.55. Almost all investigated cases were at the range of slug and plug flow regimes. Results revealed that the air-water two-phase flow could increase the heat transfer coefficient. Increment of air superficial Dean Number increased the heat transfer rate and entropy generation. A maximum increment of 35% and %26 were observed for heat transfer coefficient and entropy generation respectively. Also it was revealed that increment of VF increases the Witte-Shamsundar efficiency.

Energetic and entropic analyses of double-diffusive, forced convection heat and mass transfer in microreactors assisted with nanofluid

This paper investigates the energetic and entropic characteristics of a microchannel with thick walls. A first-order, catalytic chemical reaction is imposed on the inner surfaces of the microchannel walls, and local thermal non-equilibrium approach is employed to analyse heat transfer within the porous section of the microchannel. Further, endo-/exothermic physicochemical processes are incorporated into the fluid phase and solid structure of the microchannel. Two models describing the fluid–porous interface conditions known as Models A and B are incorporated. It is shown that for both interface models, and with the considered parametric values, the optimum thickness of the porous insert to achieve the maximum Nu is around 0.6. However, when PEC is considered, this optimum thickness may vary between 0 and 0.5. It is further shown that depending on the specification of the microreactor, either Model A or B may result in the prediction of the minimum total entropy generation rate. It is also demonstrated that by altering the endothermicity of the microreactor it is possible to find an optimal value, which minimizes the total rate of entropy generation.

Lauryl sulfate@magnetic graphene oxide nanosorbent for fast methylene blue recovery from aqueous solutions

Lauryl sulfate is utilized to functionalize magnetic graphene oxide (MGOLS) for fast removal of methylene blue (MB) using batch sorption experiments. The effects of different analytical parameters including medium pH, equilibration time, MGOLS dosage, initial MB concentration and temperature on the % MB removal are investigated. Among different isotherm and kinetic models, the experimental data were best fitted to the Langmuir and pseudo-second-order rate equations. The maximum Langmuir loading capacity reaches 624.42 mg g−1 for MGOLS under optimal conditions. Sorption kinetic of MGOLS is very fast: Approximately 96% of dye extraction was recorded within the first 2 minutes of this sorption process. The sorption mechanism is proposed and the feasibility, thermic and entropic characteristics were evaluated. Sorption and desorption performances of MGOLS are maintained almost constant over five cycles of sorption/desorption. The results concluded MGOLS as an efficient extractor for fast and feasible recovery of MB from aqueous matrices.

Геопросторова організація логістичної системи в оптимізаційній транспортній задачі

The recent publications of application of optimization and transport problem for planning the flows in logistic systems are analysed. A mathematical model of logistics system for optimizing transport problem in the region, which has a territorial division into separate elements, is build. The tools for formalized mathematical and geographical description and geospatial study of closed transportation problem are developed, knowledge of which includes four blocks. First block is the information about geolocalization of subjects (the location of territorial elements, placing of suppliers, placing of consumers, distance from suppliers to consumers, Boolean matrix of belonging suppliers to the territorial elements, Boolean matrix of belonging consumers to the territorial elements). The second block is implicative knowledge about georelativity for logistics flows between suppliers and consumers. The third block is implicative knowledge about geointegrity of subjects (suppliers and consumers) with logistics flows. The fourth block is the information about geofunctioning of subjects (annual suppliers sending, annual consumers receiving, annual transportation on traffic flows). The system and algorithms for computing of centers for centrography analysis of the functioning subjects of the transport problem and meaningful interpretation of these centers is made. A system of ordinary differential equations describing the dynamics of the operation of the optimization of the transportation problem during the year is build and its relation to classical transport problem is shown. Entropic characteristics of operation of the transportation problem optimization are described and studied and invariance of the total entropy on the subjects of the problem is shown. The directions for further research on this theme are proposed. Key words: geospatial organization, transport problem, optimization, centrography, dynamics, entropy.

Assembly of porous smectic structures formed from interlocking high-symmetry planar nanorings

Materials comprising porous structures, often in the form of interconnected concave cavities, are typically assembled from convex molecular building blocks. The use of nanoparticles with a characteristic nonconvex shape provides a promising strategy to create new porous materials, an approach that has been recently used with cagelike molecules to form remarkable liquids with "scrabbled" porous cavities. Nonconvex mesogenic building blocks can be engineered to form unique self-assembled open structures with tunable porosity and long-range order that is intermediate between that of isotropic liquids and of crystalline solids. Here we propose the design of highly open liquid-crystalline structures from rigid nanorings with ellipsoidal and polygonal geometry. By exploiting the entropic ordering characteristics of athermal colloidal particles, we demonstrate that high-symmetry nonconvex rings with large internal cavities interlock within a 2D layered structure leading to the formation of distinctive liquid-crystalline smectic phases. We show that these smectic phases possess uniquely high free volumes of up to ∼95%, a value significantly larger than the 50% that is typically achievable with smectic phases formed by more conventional convex rod- or disklike mesogenic particles.

Study of entropic characteristics of strongly correlated systems using VO2 as a model case.

To explain the huge caloric effects often observed in the first-order electronic phase transition in the strongly correlated oxides, the entropic characteristics are investigated in VO2. By evaluating the spin and charge fluctuations based on the local moment model and the Sommerfeld coefficient in the high-temperature rutile phase, it is found that these fluctuations of the high-temperature phase are the main source of the entropic change during the transition. This mode of entropic change is realized by the quenching of these fluctuations owing to the formation of a singlet bonding state in the low-temperature monoclinic phase. By introducing oxygen deficiency, a vagueness in the gap at the Fermi level is confirmed by the transport data, the X-ray photoelectron spectra and also the electronic structure calculated by the first-principles calculations. In this case, the entropic feature at the transition is weakened. Consequently, the large caloric phenomena of the strongly correlated oxides are a result of the conversion of the internal energy gain owing to the orbital selection at the ground state into the free energy gain owing to the spin and charge fluctuations at finite temperature.