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     

有源等离子体在开放大气环境下的反应扩散过程研究

利用一维模型用数值模拟的方法,研究了低气压开放环境下大气等离子体在存在等离子体源的情况下的反应扩散过程.得到了考虑化学反应、扩散以及漂移共同作用下的大气等离子体的主要成分随等离子体注入流量的变化规律及一定流量情况下主要带电成分随时空的演化规律. 将数值模拟结果与一个近似解析公式相衔接,估计达到稳态时维持一定电子密度所需要的等离子体流量,可据此进一步估计所需功率. 关键词： 大气等离子体 等离子体源 数值模拟 反应扩散过程     

弱光强空间屏蔽光伏明孤子的动态演化特性

在忽略晶体损耗和扩散效应的情况下，讨论了加外电场的光伏光折变晶体中弱光强空间屏蔽光伏明孤子及其演化特性，在弱光强条件下得到了空间屏蔽光伏明孤子的解析解表达式，与运用数值计算的方法所得到的结果十分吻合，该方法解决了以往数值求解动态演化方程时必须先数值求解常数分方程或积分方程的问题，讨论了参量失配情况下空间屏蔽光伏明孤子的动态演化特征。     

陶瓷颗粒烧结过程中气孔的扩散转移

用扩散界面相场模型研究陶瓷烧结过程中五球模型内部的气孔扩散与演化过程。采用一组随时间和空间连续变化的取向场变量和浓度场变量来表征烧结过程微结构特征,并分别用Ginzburg-Laudau动力学方程和Cahn-Hilliard动力学方程描述取向场变量和浓度场变量随时间的演化。计算模拟结果表明,陶瓷颗粒间的气孔主要是通过晶界向较大的气孔扩散聚集和颗粒外部空间扩散,这些结果与已有的陶瓷颗粒烧结实验和理论结果相符合,揭示了陶瓷颗粒烧结致密化过程的本质。     

相变换热单元动态过程的不可逆性分析

换热单元动态过程的热力学分析可为换热器的结构设计与运行参数调整提供依据。本文根据相变换热器的基本原理与质量、能量守恒方程,将相变换热器的工作过程用微分方程来表述,建立了典型相变换热单元的动态模型,得到了换热器动态过程的换热规律,进而研究了不同结构参数下换热单元动态过程的熵产变化规律。结果表明:与稳态过程相比,动态过程中产生了额外的熵产。提高金属热扩散率,降低金属壁面厚度,增加工作流体与金属壁面的换热阻力可以降低动态过程中的额外熵产。     

缓变动态Kerr-Newman黑洞的量子热力学性质

引入局域热平衡概念，用Damour-Ruffini方法和薄膜模型研究了缓变动态Kerr-Newman黑洞的Hawking辐射和熵.得到了黑洞的Hawking温度和辐射谱公式，Hawking温度随时间和视界面上的位置而变化，辐射谱为准黑体谱；计算了黑洞熵，当取与静态球对称黑洞情况相同的截断关系时便得到了黑洞的Bekenstein-Hawking熵.结果表明，缓变动态黑洞的温度是局域量，缓变动态黑洞的熵与稳态黑洞情况一样正比于黑洞视界面面积. 关键词： 缓变动态黑洞 Hawking辐射 黑洞熵     

膜动态吸附传递过程的理论分析与研究

本文针对气体透过薄膜的传质过程,基于动态吸附、扩散传递的概念,根据Langmuir界面动态吸附理论,研究了存在定向传递时表面吸附量与平衡吸附量的差异,从而将膜相传质分为吸附、内部扩散和脱附三个动态过程.讨论了界面吸附、脱附与扩散对传质阻力的不同影响,建立了薄膜传质的串联阻力模型.     

基于两节点间信息互传的量子特性

运用全量子理论,对腔耦合系统构建的两个节点,考虑节点内腔模与量子位(qubit)的耦合,结合数值计算,用熵表示信源的不确定性,对信源发出的信息进行度量,研究了两个节点相互进行信息传输过程的熵演化.通过两能级粒子与腔模的耦合强度、腔-腔之间的跃迁耦合系数和失谐量三个参数对熵变化进行分析,结论表明在共振条件下,节点间相互传输信息过程中,耦合双腔构成的两个节点熵呈现准周期性坍塌与复苏振荡变化特征,节点1与节点2熵的峰值交替出现;两个节点之间用跳跃频率λ/2π的光子作为信息传送的数椐总线,失谐使两个节点内量子位的一个频率高,一个频率低,无论先操纵哪一个量子位,在系统稳定工作状态下,量子态演化的信息传递方向总是从频率快的量子位向频率慢的量子位传递,此特性可扩展至多量子位之间量子信息的传递.用于两个节点间的远程操控.     

热加工过程中动态再结晶现象的多相场研究

金属热加工过程中的动态再结晶引起的组织演化难以通过实验实时观察, 本文基于Ginzburg-Landau动力学方程, 构造多相场法与位错密度计算相耦合的物理模型, 模拟了热加工过程中的动态再结晶现象.研究了不同温度和不同应变速率下的动态再结晶过程, 阐述了应力-应变曲线由单峰形式转变为多峰形式的原因.此外, 本文利用多相场法对多阶段变形过程进行了系统模拟, 研究了静态回复对动态再结晶过程的影响, 分析了不同的热加工参数对动态再结晶动力学的影响, 发现在变形间断过程中, 晶粒尺寸不断增大, 较高的变形温度和较低的应变速率可以加速动态再结晶过程.     

基于互信息的高动态范围成像系统成像质量分析

为了优化高动态范围成像系统的设计,完善地评价系统性能,将信息论应用于高动态范围成像系统中,把高动态范围成像系统看作通信系统,采用端到端的互信息量来评价高动态范围成像系统的成像质量.在COMS采样成像模型的基础上引入空间光调制器反射式硅基液晶的影响,建立了基于互信息的高动态范围成像系统数学模型.利用该模型分析了反射式硅基液晶与CMOS阵列像素数比、像素开口率、相对平移、相对旋转对系统互信息量的影响及造成系统成像质量下降的原因.通过仿真计算,分别得到了像素数比例、像素开口率大小、相对平移量、相对旋转角度与互信息量的相互关系曲线,并定量分析了这些因素变化对系统互信息量的影响程度.仿真结果表明反射式硅基液晶和COMS阵列的最佳匹配条件是:反射式硅基液晶和CMOS像素的占空比尽可能大,CMOS像素尺寸尽可能小,避免相对平移和相对旋转,反射式硅基液晶像素数和CMOS像素数之比为1∶1.     

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.     

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...     

Directed Data-Processing Inequalities for Systems with Feedback

We present novel data-processing inequalities relating the mutual information and the directed information in systems with feedback. The internal deterministic blocks within such systems are restricted only to be causal mappings, but are allowed to be non-linear and time varying, and randomized by their own external random input, can yield any stochastic mapping. These randomized blocks can for example represent source encoders, decoders, or even communication channels. Moreover, the involved signals can be arbitrarily distributed. Our first main result relates mutual and directed information and can be interpreted as a law of conservation of information flow. Our second main result is a pair of data-processing inequalities (one the conditional version of the other) between nested pairs of random sequences entirely within the closed loop. Our third main result introduces and characterizes the notion of in-the-loop (ITL) transmission rate for channel coding scenarios in which the messages are internal to the loop. Interestingly, in this case the conventional notions of transmission rate associated with the entropy of the messages and of channel capacity based on maximizing the mutual information between the messages and the output turn out to be inadequate. Instead, as we show, the ITL transmission rate is the unique notion of rate for which a channel code attains zero error probability if and only if such an ITL rate does not exceed the corresponding directed information rate from messages to decoded messages. We apply our data-processing inequalities to show that the supremum of achievable (in the usual channel coding sense) ITL transmission rates is upper bounded by the supremum of the directed information rate across the communication channel. Moreover, we present an example in which this upper bound is attained. Finally, we further illustrate the applicability of our results by discussing how they make possible the generalization of two fundamental inequalities known in networked control literature.     

Stochastic thermodynamics: principles and perspectives

Stochastic thermodynamics provides a framework for describing small systems like colloids or biomolecules driven out of equilibrium but still in contact with a heat bath. Both, a first-law like energy balance involving exchanged heat and entropy production entering refinements of the second law can consistently be defined along single stochastic trajectories. Various exact relations involving the distribution of such quantities like integral and detailed fluctuation theorems for total entropy production and the Jarzynski relation follow from such an approach based on Langevin dynamics. Analogues of these relations can be proven for any system obeying a stochastic master equation like, in particular, (bio)chemically driven enzyms or whole reaction networks. The perspective of investigating such relations for stochastic field equations like the Kardar-Parisi-Zhang equation is sketched as well.     

Diffusion processes with singular drift fields

A class of stochastic differential equations with highly singular drift fields is considered. Using a purely probabilistic approach, we can show the unattainability of the nodal set. Moreover, a global existence and uniqueness theorem for diffusion processes with singular drift fields is established. The finite action condition of Carlen and Zheng can be modified. We relate our results to the diffusions which describe the time evolution of quantum systems in stochastic mechanics.     

Tsallis entropy measure of noise-aided information transmission in a binary channel

Noise-aided information transmission via stochastic resonance is shown and analyzed in a binary channel by means of information measures based on the Tsallis entropy. The analysis extends the classic reference of binary information transmission based on the Shannon entropy, and also parallels a recent study based on the Rényi entropy. The conditions for a maximally pronounced stochastic resonance identify optimal Tsallis measures. The study involves a correspondence between Tsallis and Rényi information measures, specially relevant to the characterization of stochastic resonance, and establishing that for such effects identical properties are shared in common by both Tsallis and Rényi measures.     

Thermodynamic paths and stochastic order in open systems

The theorem of extremum entropy generation is related to the stochastic order of the paths inside the phase space; indeed, the system evolves, from an indistinguishable configuration to another one, on the most probable path in relation to the paths stochastic order. The result is that, at the stationary state, the entropy generation is maximal and, this maximum value is a consequence of the stochastic order of the paths in the phase space. Conversely, the stochastic order of the paths in the phase space is a consequence of the maximum of the entropy generation for the open systems at the stationary states.     

Beyond the Fourier heat conduction law and the thermal no-slip boundary condition

The problem of heat slip flow along solid walls is investigated within the framework of modern thermodynamics. The underlying idea is to elevate the heat flux at the boundary to the status of independent variable. General boundary conditions are obtained from the constraint imposed by the second law of thermodynamics expressing that the rate of entropy production is non-negative. In parallel, evolution equations for the heat flux inside the bulk of the system are also formulated.