Dynamic information theory and information description of dynamic systems

In this paper, we develop dynamic statistical information theory established by the author. Starting from the ideas that the state variable evolution equations of stochastic dynamic systems, classical and quantum nonequilibrium statistical physical systems and special electromagnetic field systems can be regarded as their information symbol evolution equations and the definitions of dynamic information and dynamic entropy, we derive the evolution equations of dynamic information and dynamic entropy that des...     

论动态信息理论

本文综述了作者的研究成果.近十年,作者将现有静态统计信息理论拓展至动态过程,建立了以表述动态信息演化规律的动态信息演化方程为核心的动态统计信息理论.基于服从随机性规律的动力学系统(如随机动力学系统和非平衡态统计物理系统)与遵守确定性规律的动力学系统(如电动力学系统)的态变量概率密度演化方程都可看成是其信息符号演化方程,推导出了动态信息(熵)演化方程.它们表明:对于服从随机性规律的动力学系统,动态信息密度随时间的变化率是由其在系统内部的态变量空间和传递过程的坐标空间的漂移、扩散和耗损三者引起的,而动态信息熵密度随时间的变化率则是由其在系统内部的态变量空间和传递过程的坐标空间的漂移、扩散和产生三者引起的.对于遵守确定性规律的动力学系统,动态信息(熵)演化方程与前者的相比,除动态信息(熵)密度在系统内部的态变量空间仅有漂移外,其余皆相同.信息和熵已与系统的状态和变化规律结合在一起,信息扩散和信息耗损同时存在.当空间噪声可略去时,将会出现信息波.若仅研究系统内部的信息变化,动态信息演化方程就约化为与表述上述动力学系统变化规律的动力学方程相对应的信息方程,它既可看成是表述动力学系统动态信息的演化规律,亦可看成是动力学系统的变化规律都可由信息方程表述.进而给出了漂移和扩散信息流公式、信息耗散率公式和信息熵产生率公式及动力学系统退化和进化的统一信息表述公式.得到了反映信息在传递过程中耗散特性的动态互信息公式和动态信道容量公式,它们在信道长度和信号传递速度之比趋于零的极限情况下变为现有的静态互信息公式和静态信道容量公式.所有这些新的理论公式和结果都是从动态信息演化方程统一推导出的.     

Dynamic statistical information theory

In recent years we extended Shannon static statistical information theory to dynamic processes and established a Shannon dynamic statistical information theory, whose core is the evolution law of dynamic entropy and dynamic information. We also proposed a corresponding Boltzmman dynamic statistical information theory. Based on the fact that the state variable evolution equation of respective dynamic systems, i.e. Fokker-Planck equation and Liouville diffusion equation can be regarded as their information symbol evolution equation, we derived the nonlinear evolution equations of Shannon dynamic entropy density and dynamic information density and the nonlinear evolution equations of Boltzmann dynamic entropy density and dynamic information density, that describe respectively the evolution law of dynamic entropy and dynamic information. The evolution equations of these two kinds of dynamic entropies and dynamic informations show in unison that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes; and that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes. Entropy and information have been combined with the state and its law of motion of the systems. Furthermore we presented the formulas of two kinds of entropy production rates and information dissipation rates, the expressions of two kinds of drift information flows and diffusion information flows. We proved that two kinds of information dissipation rates (or the decrease rates of the total information) were equal to their corresponding entropy production rates (or the increase rates of the total entropy) in the same dynamic system. We obtained the formulas of two kinds of dynamic mutual informations and dynamic channel capacities reflecting the dynamic dissipation characteristics in the transmission processes, which change into their maximum—the present static mutual information and static channel capacity under the limit case where the proportion of channel length to information transmission rate approaches to zero. All these unified and rigorous theoretical formulas and results are derived from the evolution equations of dynamic information and dynamic entropy without adding any extra assumption. In this review, we give an overview on the above main ideas, methods and results, and discuss the similarity and difference between two kinds of dynamic statistical information theories.     

通过保留相位进行全息图信息压缩的方法

从全息图的特点出发,研究了全息图的记录和再现原理,提出了一种对离轴菲涅耳全息图信息压缩的方法。对全息图进行傅里叶变换,滤除零级噪声及物光波的共轭波前,仅仅保留物光波的相位信息,而后以采用较低的采样频率对全息图重新抽样,从而大大减少了数字全息图的信息冗余。压缩后的全息图也可以获得良好像质的再现像。理论和实验均证明了该方法的可行性,为全息图的信息存贮与传输提供一条新的途径。     

高速摄影系统的信息量

根据光学信息论,得到了高速摄影系统的信息量表达式.指出:高速摄影所记录的信息量与目标、高速摄影系统的参数及使用条件有关.     

On the Kullback information measure as a basis for information theory: Comments on a proposal by Hobson and Chang

Hobson and Chang recommend that the Kullback information measure replace the Shannon information measure as a basis for information theory. They cite several items in support of their proposal. The items are considered individually and it is shown that they do not in fact constitute sufficient reasons for accepting the Hobson/Chang proposal. It is concluded that the Shannon information measure should be retained as the basis of information theory.     

On holographic information content and its compression

The present paper, based on the information theory of Shannon, studies the holographic information content, its reconstruction, and the compression of the hologram. Starting with the human binocular vision theory, it elaborates not only the information contents of the 3D object and its hologram, but also their relationship in the visual space. By proposing the particular computing method for the holographic information content and achieving meaningful results therefore, it offers the theoretical cornerstone and practical way to the reduction and compression of the holographic information content.     

遥感影像信息量与空间分辨率的关系研究

目前,关于影像信息量的研究大多是注重信息量的计算模型,很少涉及空间分辨率与信息量之间的定量关系。为了对不同空间分辨率的遥感影像进行定量化评定,以信息论和模糊数学为理论基础,信息熵为测度,通过计算不同空间分辨率水平的全色影像和多光谱影像的信息量,对信息量与空间分辨率的关系进行直接量化模拟。结果表明,影像信息量随着空间分辨率的降低呈指数降低,空间分辨率在原影像基础上每增加一倍,影像信息量相应增加3~5倍。     

非平衡统计信息理论

阐述了以表述信息演化规律的信息（熵）演化方程为核心的非平 衡统计信息理论.推导出了 Shannon信息（熵）的非线性演化方程，引入了统计物理信息并 推导出了它的非线性演化方程.这两种信息（熵）演化方程一致表明：统计信息（熵）密度 随时间的变化率是由其在坐标空间（和态变量空间）的漂移、扩散和减损（产生）三者引起 的.由此方程出发，给出了统计信息减损率和统计熵产生率的简明公式、漂移信息流和扩散 信息流的表达式，证明了非平衡系统内的统计信息减损（或增加）率等于它的统计熵产生（ 或减少）率、信息扩散与信息减损同时 关键词： 统计信息（熵）演化方程 统计信息减损率 统计熵产 生率 信息（熵）流 信息（熵）扩散 动态互信息     

Fisher information for endohedrally confined hydrogen atom

Electron localization and delocalization of endohedrally confined hydrogen atom has been investigated employing Fisher information theory. Confinement has been modeled using a spherical Gaussian-type potential. B-spline bases expansion method was used to solve the Schrödinger equation to obtain the required energy eigenvalues and the corresponding wave functions. Changes in energies with depths of potential are explained using Hellmann-Feynman theorem. The behavior of Fisher information against the confining potential depths and positions are demonstrated. Moreover, our results show that Fisher information is an effective way to measure the localization of valence electrons.     

Ion trapping for quantum information processing

In this paper we have reviewed the recent progresses on the ion trapping for quantum information processing and quantum computation. We have first discussed the basic principle of quantum information theory and then focused on ion trapping for quantum information processing. Many variations, especially the techniques of ion chips, have been investigated since the original ion trap quantum computation scheme was proposed. Full two-dimensional control of multiple ions on an ion chip is promising for the realization of scalable ion trap quantum computation and the implementation of quantum networks.      

用光学信息理论分析微弯光纤传感器的性能

通过把光学信息理论应用于微弯光纤传感器,用信息量评估测量性能,提出了一种优化系统性能和参数设计的光学信息理论。通过理论推导、直观评价和实验设计,证明了这一思想的正确性和可行性。     

Quantum information capsule in multiple-qudit systems and continuous-variable systems

Quantum correlations in an entangled many-body system are capable of storing information. Even when the information is injected by a local unitary operation to the system, the entanglement delocalizes it. In a recent study on multiple-qubit systems, it is shown that a virtual qubit defined in the correlation space plays a role of perfect storage of delocalized information, which is called a quantum information capsule (QIC). To enhance the capacity of quantum information storage, it is crucial to formulate the cases for multiple-qudit systems and continuous-variable (CV) systems. We analytically prove that it is possible to construct a QIC for general write operations of the systems. It turns out that the extension to quantum field theory is achievable. For Gaussian states, we explicitly construct a QIC for shift write operations. We analyze the time-evolution of QIC in a CV system to demonstrate the diffusion of information in entangled pure states.     

Wave vector,local momentum and local coordinate from the perspective of information theory

In the context of informational analysis of atomic and molecular systems, the connection between local quantum observables and information measures is of interest. In this paper, analytical relationships for the imaginary part of the total local momentum (coordinate) in terms of information theoretic measures have been established. Moreover, on the basis of another scheme in which the relationship among densities of information energy, Shannon entropy and Fisher information has been proposed [M. Alipour and A. Mohajeri, Mol. Phys. 110, 403 (2012)], the general formulae for the imaginary part of the total local momentum and the corresponding variance are expressed. The presented proof may be viewed in light of the relation between the local wave vector and the information energy density. Through this study, another noteworthy application of information theory is highlighted.     

一种研究二元对称离散信道平均互信息的新方法

在有干扰(噪声)无记忆信道和有记忆信道两种情况下，运用协同学的方法研究如何分配输入概率获取二元对称离散信道最大的平均互信息. 研究结果表明：对于无记忆二元对称离散信道，最大平均互信息与信息论中相同输入概率使平均互信息最大化的结果是一致的；对于干扰(噪声)有记忆二元对称离散信道，考虑输入、输出符号满足不同程度的记忆度和干扰(噪声)因子情况下，得到符号最佳输入概率. 拓展了一种研究信息论的方法. 关键词： 协同学 二元对称离散信道 互信息 转移概率     

DC-DC变换器的信息熵分析

为确定不同反馈系数k下DC-DC变换器系统的行为,结合系统处于周期状态时的稳定性和系统处于混沌时不会重复经过每一点的特点,提出了一种采用极限思想和信息熵来估计DC-DC变换器非线性行为的方法.该方法能准确分析系统处于周期状态和混沌状态的熵值,量化了DC-DC变换器倍周期分叉和混沌行为.以一阶电压反馈DCM Boost变换器和DCM Buck变换器为例进行仿真.研究结果表明,所提出的信息熵可以准确反映分叉点、周期数及产生混沌的位置,完善了该类变换器非线性动力学分析的理论和方法.     

彩虹全息系统的信息量

本文用光学信息论本征理论方法讨论了彩虹全息系统的衍射成像关系,获得了限制孔径为矩形,十字形和圆形时系统的信息量和空间自由度表达式。     

Vertical structure of predictability and information transport over the Northern Hemisphere

Based on nonlinear prediction and information theory, vertical heterogeneity of predictability and information loss rate in geopotential height field are obtained over the Northern Hemisphere. On a seasonal-to-interannual time scale, the predictability is low in the lower troposphere and high in the mid-upper troposphere. However, within mid-upper troposphere over the subtropics ocean area, there is a relatively poor predictability. These conclusions also fit the seasonal time scale. Moving to the interannual time scale, the predictability becomes high in the lower troposphere and low in the mid-upper troposphere, contrary to the former case. On the whole the interannual trend is more predictable than the seasonal trend. The average information loss rate is low over the mid-east Pacific, west of North America, Atlantic and Eurasia, and the atmosphere over other places has a relatively high information loss rate on all-time scales. Two channels are found steadily over the Pacific Ocean and Atlantic Ocean in subtropics. There are also unstable channels. The four- season influence on predictability and information communication are studied. The predictability is low, no matter which season data are removed and each season plays an important role in the existence of the channels, except for the winter. The predictability and teleconnections are paramount issues in atmospheric science, and the teleconnections may be established by communication channels. So, this work is interesting since it reveals the vertical structure of predictability distribution, channel locations, and the contributions of different time scales to them and their variations under different seasons.     

Quantum information capsule and information delocalization by entanglement in multiple-qubit systems

Where do entangled multiple-qubit systems store information? For information injected into a qubit, this question is nontrivial and interesting since the entanglement delocalizes the information. So far, a common picture is that of a qubit and its purification partner sharing the information quantum mechanically. Here, we introduce a new picture of a single qubit in the correlation space, referred to as quantum information capsule (QIC), confining the information perfectly. This picture is applicable for the entangled multiple-qubit system in an arbitrary state. Unlike the partner picture, in the QIC picture, by swapping the single-body state, leaving other subsystems untouched, the whole information can be retrieved out of the system. After the swapping process, no information remains in the system.