利用同质异位素产额比提取对称能的近似方法

在修改的Fisher模型框架下, 利用同质异位素产额比和结合能方程中对称能系数与温度比率的关联, 可以提取对称能系数与温度的比值。 利用3种不同的近似方法得到了重离子核反应产生丰中子余核的对称能系数与温度比（a_sym/T）,并研究了相关物理量对a_sym/T的影响。结果表明, 库仑能对提取丰中子余核的a_sym/T影响较小,且参考核的选取对a_sym/T的提取也有一定的影响。 In the framework of the modified Fisher model, correlations between the symmetry energy coefficient in semi classical mass formula to temperature (a_sym/T) and the isobaric yield ratio in Heavy ion collisions are established. a_sym/Tof neutron rich fragments are extracted using these correlations. It is found that the Coulomb energy term has little effect on a_sym/T of fragments, while the reference isobars adopted have great influence on the extracted a sym/T of fragments.     

Maximum Shannon Entropy, Minimum Fisher Information, and an Elementary Game

We formulate an elementary statistical game which captures the essence of some fundamental quantum experiments such as photon polarization and spin measurement. We explore and compare the significance of the principle of maximum Shannon entropy and the principle of minimum Fisher information in solving such a game. The solution based on the principle of minimum Fisher information coincides with the solution based on an invariance principle, and provides an informational explanation of Malus' law for photon polarization. There is no solution based on the principle of maximum Shannon entropy. The result demonstrates the merits of Fisher information, and the demerits of Shannon entropy, in treating some fundamental quantum problems. It also provides a quantitative example in support of a general philosophy: Nature intends to hide Fisher information, while obeying some simple rules.     

Anomalous Isotopic Frequency Ratio of the Stretching (N+H) Vibrations in Ion Pairs

Abstract

Earlier, when investigating H-complexes of the RO-H…BR₁ type in solutions ^1–3 and crystalline state ⁴, the isotopic shift for frequencies of the stretching vibrations (OH) at substitution of H for D was shown to systematically decrease with increased strength of the H-bond. In strong H-complexes, the (OH) and (OD) bands in the i.r. spectra have a complex structure: depending on the strength of the H-complex in a wide range of frequencies (3000–1000 cm^?1), several submaxima caused by a Fermi-resonance interaction of the fundamental tone of (OH) with combinations and overtones in the bending vibrations of R-O-H were observed ^1–5. Hence, the frequencies and intensities of the (OH) and (OD) bands in strong H-complexes should be considered as corresponding to the gravity centre (°) and overall intensity (A°) of all the     

The Fisher information measure and Shannon entropy for particulate matter measurements

We investigated the dynamics of particulate matter data, recorded in Tito, a small industrial area of southern Italy. The analysis of these signals was performed using the Fisher information measure (FIM), which is a powerful tool for investigating complex and nonstationary signals, and the Shannon entropy, which is a well-known tool for investigating the degree of disorder in dynamical systems. Our results point to an increase of disorder and complexity from fine to coarse particulates.     

Onicescu information energy in terms of Shannon entropy and Fisher information densities

Following recent studies concerning the use of information theory in electronic structure theory of atomic and molecular systems, an analytical relationship between Onicescu information energy and densities of Shannon entropy and the two forms of the Fisher information has been presented. The established proof must be viewed in the light of the exponentially decaying nature of the asymptotic density of atoms and molecules.     

An Isoratio Method to Study Free Energy and Temperature Effects in Intermediate Mass Fragments Produced in Heavy-Ion Collisions

An isoratio method, i.e., the isotopic (isotonic) ratio among three isotopes (isotones), is proposed to study the free energy and temperature effects in the intermediate mass fragments produced in heavy-ion collisions. The parameterizations for the free energy of nucleus at low temperature, which have been proposed in the framework of the density functional theory using the SKM skymre interaction, are adopted to calculate the temperature-dependent free energy of fragment. By analyzing the measured yields of fragments in the 140A MeV ^58,64Ni + ⁹Be reactions, it is verified that the free energy in the isoratio is almost the same for different reactions. A temperature-dependent pairing-energy is introduced into the parameterizations for free energy, which reveals that the weakened pairing energy at the low temperature accounts for the weakened or disappearing odd-even staggering in isoratio.     

Shannon entropies and Fisher information of K-shell electrons of neutral atoms

We represent the two K-shell electrons of neutral atoms by Hylleraas-type wave function which fulfils the exact behavior at the electron–electron and electron-nucleus coalescence points and, derive a simple method to construct expressions for single-particle position- and momentum-space charge densities, $\rho (\mathit{r})$ and $\gamma (\mathit{p})$ respectively. We make use of the results for $\rho (\mathit{r})$ and $\gamma (\mathit{p})$ to critically examine the effect of correlation on bare (uncorrelated) values of Shannon information entropies (S) and of Fisher information (F) for the K-shell electrons of atoms from helium to neon. Due to inter-electronic repulsion the values of the uncorrelated Shannon position-space entropies are augmented while those of the momentum-space entropies are reduced. The corresponding Fisher information are found to exhibit opposite behavior in respect of this. Attempts are made to provide some plausible explanation for the observed response of S and F to electronic correlation.     

Entropy,Fisher Information and Variance with Frost-Musulin Potenial

This study presents the Shannon and Renyi information entropy for both position and momentum space and the Fisher information for the position-dependent mass Schrödinger equation with the Frost-Musulin potential. The analysis of the quantum mechanical probability has been obtained via the Fisher information. The variance information of this potential is equally computed. This controls both the chemical properties and physical properties of some of the molecular systems. We have observed the behaviour of the Shannon entropy. Renyi entropy, Fisher information and variance with the quantum number n respectively.     

Information theories for time-dependent harmonic oscillator

Information theories for the general time-dependent harmonic oscillator are described on the basis of invariant operator method. We obtained entropic uncertainty relation of the system and discussed whether it is always larger than or equal to the physically allowed minimum value. Shannon information and Fisher information are derived by means of density operator that satisfies Liouville–von Neumann equation and their characteristics are investigated. Shannon information is independent of time, but Fisher information is explicitly dependent on time as the time functions of the Hamiltonian vary. We can regard that the Fisher information is a local measure since its time behavior is largely affected by local arrangements of the density, whilst the Shannon information plays the role of a global measure of the spreading of density. To promote the understanding, our theory is applied to special systems, the so-called quantum oscillator with time-dependent frequency and strongly pulsating mass system.     

Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks

Non-Hermitian topological edge states have many intriguing properties, however, to date, they have mainly been discussed in terms of bulk–boundary correspondence. Here, we propose using a bulk property of diffusion coefficients for probing the topological states and exploring their dynamics. The diffusion coefficient was found to show unique features with the topological phase transitions driven by parity–time (PT)-symmetric non-Hermitian discrete-time quantum walks as well as by Hermitian ones, despite the fact that artificial boundaries are not constructed by an inhomogeneous quantum walk. For a Hermitian system, a turning point and abrupt change appears in the diffusion coefficient when the system is approaching the topological phase transition, while it remains stable in the trivial topological state. For a non-Hermitian system, except for the feature associated with the topological transition, the diffusion coefficient in the PT-symmetric-broken phase demonstrates an abrupt change with a peak structure. In addition, the Shannon entropy of the quantum walk is found to exhibit a direct correlation with the diffusion coefficient. The numerical results presented herein may open up a new avenue for studying the topological state in non-Hermitian quantum walk systems.     

A comparison of the Shannon and Kullback information measures

Two widely used information measures are compared. It is shown that the Kullback measure, unlike the Shannon measure, provides the basis for a consistent theory of information which extends to continuous sample spaces and to nonconstant prior distributions. It is shown that the Kullback measure is a generalization of the Shannon measure, and that the Kullback measure has more reasonable additivity properties than does the Shannon measure. The results lend support to Jaynes's entropy maximization procedure.     

共焦扫描荧光显微镜的信噪比与信息量

在研制用于对厚的生物样品进行光学断层成像的共焦扫描荧光显微镜时，由于成像信号十分微弱及存在很强的多次散射作用，因此杂散光的抑制非常重要，而信噪比、信号背景比就成为决定能否获得高对比度、高分率图像的关键。运用光学信息量的概念，在已有的光学成像系统信息量计算、共焦扫描荧光显微镜信噪比及传递函数计算的基础上，详细分析了共焦扫描荧光显微镜信息量与信噪比等之间的定量关系。该关系表明，为了充分利用共焦扫描荧光显微镜的成像性能，必须选择适当的探测小孔。所得的结果对于共焦扫描荧光显微成像系统的研制有重要的实用价值。     

Metabolic and Isotopic Correlations between D-Glucose,L-Ascorbic Acid and L-Tartaric Acid

Abstract

L-Ascorbic acid in fruit juices is enriched in ¹³C by 4.8 δ-units relative to its precursor glucose, and this enrichment is mainly located in position C-1. On the other hand, biotechnologically produced L-ascorbic acid preserves the pattern as expected from glucose. In grapes L-tartaric acid is synthesized from glucose via L-ascorbic acid and it is one of its main products. It preserves C-atoms 1 to 4 from glucose and the measured δ¹³C-value is identical to that calculated from this precursor.

The findings are interpreted as overlapping influences of isotope discriminations after metabolic branching and relative turnover rates leading to isotopic balances. The results can also be used to distinguish between identical products by different synthetic processes.     

Fisher Information and Complexity Measure of Generalized Morse Potential Model

The spreading of the quantum-mechanical probability distribution density of the three-dimensional system is quantitatively determined by means of the local information-theoretic quantity of the Shannon information and information energy in both position and momentum spaces. The complexity measure which is equivalent to Cramer-Rao uncertainty product is determined. We have obtained the information content stored, the concentration of quantum system and complexity measure numerically for n=0, 1, 2 and 3 respectively.     

Information and the Brukner-Zeilinger Interpretation of Quantum Mechanics: A Critical Investigation

In Brukner and Zeilinger's interpretation of quantum mechanics, information is introduced as the most fundamental notion and the finiteness of information is considered as an essential feature of quantum systems. They also define a new measure of information which is inherently different from the Shannon information and try to show that the latter is not useful in defining the information content in a quantum object. Here, we show that there are serious problems in their approach which make their efforts unsatisfactory. The finiteness of information does not explain how objective results appear in experiments and what an instantaneous change in the so-called information vector (or catalog of knowledge) really means during the measurement. On the other hand, Brukner and Zeilinger's definition of a new measure of information may lose its significance, when the spin measurement of an elementary system is treated realistically. Hence, the sum of the individual measures of information may not be a conserved value in real experiments.     

Shannon and Fisher entropies for a hydrogen atom under soft spherical confinement

We calculate Shannon and Fisher entropies in the position and momentum space, and some complexity measures for a variationally described hydrogen atom confined in soft and hard spherical boxes of varying dimension $r_c$ and selected values of strength $U_0$. We include calculations for a free particle trapped in impenetrable boxes. It is found that the Shannon entropy $S_r$ becomes negative for small cavity radii and large values of $U_0$, due to the highly localized nature of the particle. For soft confinement and small cavity dimensions, the entropies change very rapidly over short radial intervals.     

Quantum Fisher Information and Uncertainty Relations

It is well known that the Cramér–Rao inequality places a lower bound for quantum Fisher information in terms of the variance of any quantum measurement. We establish an upper bound for quantum Fisher information of a parameterized family of density operators in terms of the variance of the generator. These two bounds together yield a generalization of the Heisenberg uncertainty relations from statistical estimation perspective.     

Real and spurious contributions for the Shannon, Rényi and Tsallis entropies

A two-parameter probability distribution is constructed by dilatation (or contraction) of the escort probability distribution. This transformation involves a physical probability distribution P associated with the system under study and an almost arbitrary reference probability distribution P^′. In contrast to the Shannon and Rényi entropies, the Tsallis entropy does not decompose as the sum of the physical contribution due to P and the reference or spurious part owing to P^′. For solving this problem, a slight modification to the relation between Tsallis and Rényi entropies must be introduced. The procedure in this paper gives rise to a nonconventional one-parameter Shannon entropy and to two-parameter Rényi and Tsallis entropies associated with P. It also contributes to clarify the meaning and role of the escort probabilities set.     

Differential Entropy and Dynamics of Uncertainty

We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The Shannon entropy validity is extended to probability distributions inferred from L ²(R ⁿ ) quantum wave packets. In contrast to the von Neumann entropy which simply vanishes on pure states, the differential entropy quantifies the degree of probability (de)localization and its time development. The associated dynamics of the Fisher information functional quantifies nontrivial power transfer processes in the mean, both in dissipative and quantum mechanical cases. PACS NUMBERS: 05.45.+b, 02.50.-r, 03.65.Ta, 03.67.-a     

Entropy Method for Decision-Making: Uncertainty Cycles in Tourism Demand

A new methodology is presented for measuring, classifying and predicting the cycles of uncertainty that occur in temporary decision-making in the tourist accommodation market (apartments and hotels). Special attention is paid to the role of entropy and cycles in the process under the Adaptive Markets Hypothesis. The work scheme analyses random cycles from time to time, and in the frequency domain, the linear and nonlinear causality relationships between variables are studied. The period analysed is from January 2005 to December 2018; the following empirical results stand out: (1) On longer scales, the periodicity of the uncertainty of decision-making is between 6 and 12 months, respectively, for all the nationalities described. (2) The elasticity of demand for tourist apartments is approximately 1% due to changes in demand for tourist hotels. (3) The elasticity of the uncertainty factor is highly correlated with the country of origin of tourists visiting Spain. For example, it has been empirically shown that increases of 1% in uncertainty cause increases in the demand for apartments of 2.12% (worldwide), 3.05% (UK), 1.91% (Germany), 1.78% (France), 7.21% (Ireland), 3.61% (The Netherlands) respectively. This modelling has an explanatory capacity of 99% in all the models analysed.