On the thermodynamics of plasticity during quasi-isentropic compression of metallic glass

Entropy production in quasi-isentropic compression (QIC) is critically important for understanding the properties of materials under extremeconditions. However, the origin and accurate quantification of entropy in this situation remain long-standing challenges. In this work, a framework is established for the quantification of entropy production and partition, and their relation to microstructural change in QIC. Cu50Zr50is taken as a model material, and its compression is simulated by molecular dynamics. On the basis of atomistic simulation-informed physicalproperties and free energy, the thermodynamic path is recovered, and the entropy production and its relation to microstructural change aresuccessfully quantified by the proposed framework. Contrary to intuition, entropy production during QIC of metallic glasses is relativelyinsensitive to the strain rate ˙γ when ˙γ ranges from 7.5 × 10^(8) to 2 × 10^(9)/s, which are values reachable in QIC experiments, with a magnitudeof the order of 10^(−2)kB/atom per GPa. However, when ˙γ is extremely high (>2 × 10^(9)/s), a notable increase in entropy production rate with˙γ is observed. The Taylor–Quinney factor is found to vary with strain but not with strain rate in the simulated regime. It is demonstrated thatentropy production is dominated by the configurational part, compared with the vibrational part. In the rate-insensitive regime, the increase inconfigurational entropy exhibits a linear relation to the Shannon-entropic quantification of microstructural change, and a stretched exponential relation to the Taylor–Quinney factor. The quantification of entropy is expected to provide thermodynamic insights into the fundamentalrelation between microstructure evolution and plastic dissipation.

Entropies of the Y-Junction Type Nanostructures

Recent research on nanostructures has demonstrated their importance and application in a variety of fields.Nanostructures are used directly or indirectly in drug delivery systems,medicine and pharmaceuticals,biological sensors,photodetectors,transistors,optical and electronic devices,and so on.The discovery of carbon nanotubes with Y-shaped junctions is motivated by the development of future advanced electronic devices.Because of their interactionwithY-junctions,electronic switches,amplifiers,and three-terminal transistors are of particular interest.Entropy is a concept that determines the uncertainty of a system or network.Entropy concepts are also used in biology,chemistry,and applied mathematics.Based on the requirements,entropy in the form of a graph can be classified into several types.In 1955,graph-based entropy was introduced.One of the types of entropy is edgeweighted entropy.We examined the abstract form of Y-shaped junctions in this study.Some edge-weight-based entropy formulas for the generic view of Y-shaped junctions were created,and some edge-weighted and topological index-based concepts for Y-shaped junctions were discussed in the present paper.

Standard-state entropies and their impact on the potential-dependent apparent activation energy in electrocatalysis

The apparent activation energy,Eapp,is a common measure in thermal catalysis to discuss the activity and limiting steps of catalytic processes on solid-state materials.Recently,the electrocatalysis community adopted the concept of Eappand combined it with the Butler-Volmer theory.Certain observations though,such as potential-dependent fluctuations of Eapp,are yet surprising because they conflict with the proposed linear decrease in Eappwith increasing overpotential.The most common explanation for this finding refers to coverage changes upon alterations in the temperature or the applied electrode potential.In the present contribution,it is demonstrated that the modulation of surface coverages cannot entirely explain potential-dependent oscillations of Eapp,and rather the impact of entropic contributions of the transition states has been overlooked so far.In the case of a nearly constant surface coverage,these entropic contributions can be extracted by a dedicated combination of Tafel plots and temperature-dependent experiments.

Energetic and Entropic Changes in Volume Work and Chemical Reactions

In the present study, energetic and entropic changes are investigated on a comparative basis, as they occur in the volume changes of an ideal gas in the Carnot cycle and in the course of the chemical reaction in a lead-acid battery. Differences between reversible and irreversible processes have been worked out, in particular between reversibly exchanged entropy (∆eS) and irreversibly produced entropy (∆iS). In the partially irreversible case, ∆eS and ∆iS add up to the sum ∆S for the volume changes of a gas, and only this function has an exact differential. In a chemical reaction, however, ∆eS is independent on reversibility. It arises from the different intramolecular energy contents between products and reactants. Entropy production in a partially irreversible Carnot cycle is brought about through work-free expansions, whereas in the irreversible battery reaction entropy is produced via activated complexes, whereby a certain, variable fraction of the available chemical energy becomes transformed into electrical energy and the remaining fraction dissipated into heat. The irreversible reaction process via activated complexes has been explained phenomenologically. For a sufficiently high power output of coupled reactions, it is essential that the input energy is not completely reversibly transformed, but rather partially dissipated, because this can increase the process velocity and consequently its power output. A reduction of the counter potential is necessary for this purpose. This is not only important for man-made machines, but also for the viability of cells.

Analytical Fitting Functions of Finite Sample Discrete Entropies of White Gaussian Noise

In order to find the convergence rate of finite sample discrete entropies of a white Gaussian noise(WGN), Brown entropy algorithm is numerically tested.With the increase of sample size, the curves of these finite sample discrete entropies are asymptotically close to their theoretical values.The confidence intervals of the sample Brown entropy are narrower than those of the sample discrete entropy calculated from its differential entropy, which is valid only in the case of a small sample size of WGN. The differences between sample Brown entropies and their theoretical values are fitted by two rational functions exactly, and the revised Brown entropies are more efficient. The application to the prediction of wind speed indicates that the variances of resampled time series increase almost exponentially with the increase of resampling period.

Quantum information entropies of the eigenstates for the Pschl-Teller-like potential

Shannon entropy for lower position and momentum eigenstates of Ptschl-Teller-like potential is evaluated. Based on the entropy densities demonstrated graphically, we note that the wave through of the position information entropy density p （x） moves right when the potential parameter V1 increases and its amplitude decreases. However, its wave through moves left with the increase in the potential parameter 丨V2丨. Concerning the momentum information entropy density p（p）, we observe that its amplitude increases with increasing potential parameter V1, but its amplitude decreases with increasing丨V2丨. The Bialynicki-Birula-Mycielski （BBM） inequality has also been tested for a number of states. Moreover, there exist eigenstates that exhibit squeezing in the momentum information entropy. Finally, we note that position information entropy increases with V1, but decreases with 丨V2丨, However, the variation of momentum information entropy is contrary to that of the position information entropy.

Complexity analysis and dynamic characteristics of EEG using MODWT based entropies for identification of seizure onset

In this paper,complexity analysis and dynamic characteristics of electroencephalogram(EEG) signal based on maximal overlap discrete wavelet transform(MODWT) has been exploited for the identification of seizure onset.Since wavelet-based studies were well suited for classification of normal and epileptic seizure EEG,we have applied MODWT which is an improved version of discrete wavelet transform(DWT).The selection of optimal wavelet sub-band and features plays a crucial role to understand the brain dynamics in epileptic patients.Therefore,we have investigated MODWT using four different wavelets,namely Haar,Coif4,Dmey,and Sym4 sub-bands until seven levels.Further,we have explored the potentials of six entropies,namely sigmoid,Shannon,wavelet,Renyi,Tsallis,and Steins unbiased risk estimator(SURE) entropies in each sub-band.The sigmoid entropy extracted from Haar wavelet in sub-band D4 showed the highest accuracy of 98.44% using support vector machine classifier for the EEG collected from Ramaiah Medical College and Hospitals(RMCH).Further,the highest accuracy of 100% and 94.51% was achieved for the University of Bonn(UBonn) and CHB-MIT databases respectively.The findings of the study showed that Haar and Dmey wavelets were found to be computationally economical and expensive respectively.Besides,in terms of dynamic characteristics,MODWT results revealed that the highest energy present in sub-bands D2,D3,and D4 and entropies in those respective sub-bands outperformed other entropies in terms of classification results for RMCH database.Similarly,using all the entropies,sub-bands D5 and D6 outperformed other sub-bands for UBonn and CHB-MIT databases respectively.In conclusion,the comparison results of MODWT outperformed DWT.

IONIC ENTROPIES ON A BOND PARAMETER SCALE

Some expressions were proposed in the previous report to exp-ress the relation between the entropies S°298 and the bond parameterZ/r in the same type of compounds.Based on this we derived a rela-tion formula for calculating the ionic entropies and established a

Shannon information entropies for rectangular multiple quantum well systems with constant total lengths

We first study the Shannon information entropies of constant total length multiple quantum well systems and then explore the effects of the number of wells and confining potential depth on position and momentum information entropy density as well as the corresponding Shannon entropy.We find that for small full width at half maximum（FWHM） of the position entropy density,the FWHM of the momentum entropy density is large and vice versa.By increasing the confined potential depth,the FWHM of the position entropy density decreases while the FWHM of the momentum entropy density increases.By increasing the potential depth,the frequency of the position entropy density oscillation within the quantum barrier decreases while that of the position entropy density oscillation within the quantum well increases.By increasing the number of wells,the frequency of the position entropy density oscillation decreases inside the barriers while it increases inside the quantum well.As an example,we might localize the ground state as well as the position entropy densities of the1 st,2 nd,and 6 th excited states for a four-well quantum system.Also,we verify the Bialynicki–Birula–Mycieslki（BBM）inequality.

Practical Method of Estimating Standard Entropies of Cations in Solid Compounds

The standard entropy Sm of the cation in solid compound is represented by using the greatest principal quantum number (n) and electron number (m) of the highest energy level group in ground state atom. There is a high correlativity between Sm and n, m, with the coefficient of multiple correlation being 0. 993. The binary linear regres siou equation Sm = 8. 58+ 8. 03n+ 0. 33m is built up by the least square method, and proved highly effective by the F test under the significance level a= 0. 01. The correlativity between Sm and m increases with the increase of n.

A New Model for Calculation of Standard Entropies of Solid Compounds Ⅳ-Calculation of Standard Entropies of Solid Complex Silicates S

This paper presents a new model for the calculation of the standard entropies of solidcomplex silicates as follows.4. =53.63+9914-72.81 J/kmol (R=0.9915, Sd=5.39)Sixty complex silicates have been investigated, and good agreement was found between theestimated and experimental entropy values.

Shannon information entropies for position-dependent mass Schrdinger problem with a hyperbolic well

The Shannon information entropy for the Schrodinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are broken when recovered to original space x. The position Sx and momentum S p information entropies for six low-lying states are calculated. We notice that the Sx decreases with the increasing mass barrier width a and becomes negative beyond a particular width a,while the Sp first increases with a and then decreases with it. The negative Sx exists for the probability densities that are highly localized. We find that the probability density ρ（x） for n = 1, 3, 5 are greater than 1 at position x = 0. Some interesting features of the information entropy densities ρs（x） and ρs（p） are demonstrated. The Bialynicki-Birula-Mycielski（BBM）inequality is also tested for these states and found to hold.

Thermodynamical and Statistical-Mechanical Entropies of the General Static Spherically Symmetric Black Hole

The thermodynamical entropy of the general four-dimensional static spherically symmetric black hole is obtained by using the Euclidean path integral approach of Gibbons-Hawking,and its statistical-mechanical entropy is calculated according to the brick wall model of’t Hooft.It is shown that the two entropies are not identical in general and the difference between them depends on the area of the horizon and the Ricci scalar curvature on the event horizon.

Quantum entropies of electromagnetic and gravitational fields on Taub-NUT black hole background

The main characteristics and Petrov type of Taub-NUT spacetime are studied, and the quantum entropy of Taub-NUT black hole due to electromagnetic and gravitational fields is calculated via brick-wall model. It is shown that the quantum entropy has both the linearly and the logarithmically divergent terms. For electromagnetic field, these terms depend on the characteristic of the black hole; while for gravitational field, they depend not only on the characteristic of the black hole but also on the spin of the fields.

THE NEW MODEL FOR CALCULATION OF STANDARD ENTROPIES OF SOLID COMPOUNDS Ⅲ CALCULATION FOR STANDARD ENTROPIES OF SOLID BINARY OXIDES

This paper establishes a new model for calculation of the standard entropies of solid binary oxides as follows: S_(29)=27.07×Φ_1+1.120×Φ_2+n_1×k×Φ, -22.19 e.u (R=0.9960) We have invesigated 103 binary oxides. and found good agreemenl between estimated and experimental entropies.

Basic Entropies for Positive-Definite Matrices

We extend basic entropies in the classical information theory to matrix ones in the quantum information theory. Then we show that relations between matrix entropies similar to the classical ones hold.

Analysis of entropies based on empirical mode decomposition in amnesic mild cognitive impairment of diabetes mellitus

EEG characteristics that correlate with the cognitive functions are important in detecting mild cognitive impairment(MCI)in T2DM.To investigate the complexity between aMCI group and age-matched non-aMCI control group in T2DM,six entropies combining empirical mode decomposition(EMD),including Approximate entropy(ApEn),Sample entropy(SaEn),Fuzzy entropy(FEn),Permutation entropy(PEn),Power spectrum entropy(PsEn)and Wavelet entropy(WEn)were used in the study.A feature extraction technique based on maximization of the area under the curve(AUC)and a support vector machine(SVM)were subsequently used to for features selection and classi¯cation.Finally,Pearson's linear correlation was employed to study associations between these entropies and cognitive functions.Compared to other entropies,FEn had a higher classification accuracy,sensitivity and specificity of 68%,67.1% and 71.9%,respectively.Top 43 salient features achieved classification accuracy,sensitivity and speci¯city of 73.8%,72.3% and 77.9%,respectively.P4,T4 and C4 were the highest ranking salient electrodes.Correlation analysis showed that FEn based on EMD was positively correlated to memory at electrodes F7,F8 and P4,and PsEn based on EMD was positively correlated to Montreal cognitive assessment(MoCA)and memory at electrode T4.In sum,FEn based on EMD in righttemporal and occipital regions may be more suitable for early diagnosis of the MCI with T2DM.

THE ENTROPIES OF THE COLLAPSING STAR AND OF THE BLACK HOLE

We put forth three modes of black hole formation, i.e. (1) A black hole kern forms initially inside the collapsing star. (2) The different mass shells of the collapsing star fulfils the Schwarzschild condition simultaneously. (3) Only the outmost mass shell of the collapsing star fulfils the Schwarzschild condition. We then calculate the entropy of the collapsing star for modes (1) and (3) and find that they are only 10-19 times the entropy of black hole. Modes (1) may be occure during the supernova explosions or galaxy explosions. Mode (3) may be occur in the formation of galactic black hole.

Expanded Relative Operator Entropies and Operator Valued α-Divergence

For strictly positive operators A and B, and for x ∈ [0,1] and r ∈[-1,1], we investigate the operator power mean A#x,rB=A1/2{（1-x）/＋x（a-1＊2BA-1/2）r}1/rA1/2 If r = O, this is reduced to the geometric operator mean A#x,rB=A1/2{（1-x）/＋x（a-1＊2BA-1/2）r}1/rA1/2 Since A #0,r B = A and A #l,r B = B, weregard A#t,rB as apath combining A and B.Our aim is to show the essential properties of St,r （AIB）. The Tsallis relative operator entropy by Yanagi, Kuriyama and Furuichi can also be expanded, and by using this, we can give an expanded operator valued a-divergence and obtain its properties.

Category Theoretic Properties of the A. Rényi and C. Tsallis Entropies

The problem of embedding the Tsallis, Rényi and generalized Rényi entropies in the framework of category theory and their axiomatic foundation is studied. To this end, we construct a special category MES related to measured spaces. We prove that both of the Rényi and Tsallis entropies can be imbedded in the formalism of category theory by proving that the same basic partition functional that appears in their definitions, as well as in the associated Lebesgue space norms, has good algebraic compatibility properties. We prove that this functional is both additive and multiplicative with respect to the direct product and the disjoint sum (the coproduct) in the category MES, so it is a natural candidate for the measure of information or uncertainty. We prove that the category MES can be extended to monoidal category, both with respect to the direct product as well as to the coproduct. The basic axioms of the original Rényi entropy theory are generalized and reformulated in the framework of category MES and we prove that these axioms foresee the existence of an universal exponent having the same values for all the objects of the category MES. In addition, this universal exponent is the parameter, which appears in the definition of the Tsallis and Rényi entropies. It is proved that in a similar manner, the partition functional that appears in the definition of the Generalized Rényi entropy is a multiplicative functional with respect to direct product and additive with respect to the disjoint sum, but its symmetry group is reduced compared to the case of classical Rényi entropy.