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     

大量粒子系统的课程教学体系探讨

本文讨论了分布函数的概念、分布函数与熵的联系和最大熵原理。阐述了引入信息熵与最大熵原理对于大量粒子系统的课程教学体系改革的必要性和重要性。     

Information dynamics: temporal behavior of uncertainty measures

We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tools are the information theory methods and inequalities satisfied by Fisher and Shannon information measures. We focus on the compatibility of these inequalities with the prescribed (deterministic, random or quantum) temporal behavior of pertinent probability densities.      

A new theorem of information theory

Consider a random experiment whose possible outcomes arez ₁,z ₂,...,z _n. Let the prior probabilities be p₁ ⁰, ...,p_n ⁰, and let the posterior probabilities bep ₁,...,p _n. It is shown that, subject to certain prescribed and intuitively reasonable conditions, the expressionI =k p _i In (p _i/p _i ⁰), wherek is a positive constant, is the unique expression for the information contained in a message which alters the probabilities from thep _i ⁰ to thep _i.     

中子裂变链统计涨落问题的数值计算方法

研究了弱中子源驱动下,裂变系统中子裂变链统计涨落问题的数值计算方法。进行了数值计算建模、数值方法分析、数值计算检验、一类问题概率分布函数的统计涨落特征量的数值计算示范。特例数值检验表明:只要数值解方程组阶数(截断) N足够大,数值解满足归一(守恒) 律、指数增长律,并与精确解析解一致。对于非定常裂变系统中子裂变链统计涨落问题提出了一维等效模型下数值模拟的方法。     

The crossover from classical to quantum regime in the problem of the decay of the metastable state

The probability of the decay of the metastable state has been found as a function of viscosity and temperature. At low temperatures, a classical overbarrier transition changes to the quantum tunneling. At low viscosity in classical and transitive semiquantum region of temperatures a depopulation of the distribution function is significant. The distribution function is shown to satisfy the integral kinetic equation, the kernel of which equals the transition probability. The probability of transitions, induced by the red noise, with the frequency comparable to the transition frequency, is found.     

粉尘云电火花最小点火能的统计分析

基于统计分析的Logistic回归模型,应用以概率表示粉尘云最小点火能的计算方法,在容积为1.28 L的Mike 3管内对不同浓度的烟酸粉尘-空气混合物进行了最小点火能测试实验,利用SPSS软件计算得到了各浓度下烟酸粉尘云点火成功概率为10%和50%时的最小点火能。结果表明,烟酸粉尘云最小点火能随浓度的增大呈现先减小后增大的趋势,最后保持在一定的能量范围内。与其他标准的计算结果相比,这种方法给出的结果更符合实际情况,也能满足不同生产环境对安全控制的需要。

     

Imaging of an Absorbing Object Embedded in a Dense Scattering Medium by Diffusing Light Topography

A new and simple imaging method for an absorbing object embedded in a dense scattering medium is proposed. The distinct characteristic is the positive usage of the diffusing light in the dense scattering medium to image the absorbing object. The principle is based on the equivalence between a probability distribution function of the path-length and a backscattered intensity distribution integrated spatially in the boundary plane between the medium and the air. The usefulness of the proposed method is experimentally confirmed for a modified pyramidal object painted black and thin tubes filled with black and red inks. The conditions under which the better image can be reconstructed are confirmed from the results of experiments and simulations. It is finally shown that our proposed method is capable of imaging the map of blood vessels distributed under the skin layers.     

On the phase space approach to complexity

We elaborate in some detail on a new phase space approach to complexity, due to Y.-C. Zhang. We show in particular that the connection between maximal complexity and power law noise or correlations can be derived from a simple variational principle. For a 1D signal we find 1/f noise, in accordance with Zhang.     

Modified scaling relation for the random-field Ising model

We investigate the low-temperature critical behavior of the three-dimensional random-field Ising ferromagnet. By a scaling analysis we find that in the limit of temperature T → 0 the usual scaling relations have to be modified as far as the exponent α of the specific heat is concerned. At zero temperature, the Rushbrooke equation is modified to α + 2β + γ = 1, an equation which we expect to be valid also for other systems with similar critical behavior. We test the scaling theory numerically for the three-dimensional random-field Ising system with Gaussian probability distribution of the random fields by a combination of calculations of exact ground states with an integer optimization algorithm and Monte Carlo methods. By a finite-size scaling analysis we calculate the critical exponents ν ≈ 1.0, β ≈ 0.05,

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≈ 2.9, γ ≈ 1.5 and α ≈ −0.55.     

黑体辐射公式的多种推导及其在近代物理构建中的意义(Ⅰ)

黑体辐射是近代物理史上一只会下金蛋的鹅,是近代物理的摇篮。黑体辐射研究的意义还在于这是唯一一个涉及c,k,h三个普适常数的物理情景。黑体辐射谱抗测量误差的特性带来了辐射标准和绝对温度参照,谱分布公式对模型的不敏感则使得黑体辐射成为独特的物理研究母题。黑体辐射谱分布公式,普朗克多角度推导过,德拜推导过,艾伦菲斯特推导过,劳厄推导过,洛伦兹和庞加莱深入讨论过,泡利推导过,玻色推导过,爱因斯坦在20多年的时间里多角度推导过且产出最为丰硕,近代还有从相对论角度的推导,每一个角度的推导都带来了物理学的新内容,这包括量子力学、固体量子论、受激辐射、量子统计、相对论统计,等等。认真回顾黑体辐射研究的历史细节,考察其中的思想概念演化,不啻于体验一次教科书式的学(做)物理之旅,比如也可以尝试给出能量局域分立化的简单新证明。