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Dynamic information theory and information description of dynamic systems

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Science china(physics,Mechanics & Astronomy) 2010年第4期53卷 607-627页

作者： xing XiuSan Department of physics, beijing institute of technology, beijing 100081, china beijing institute of technology Department of Physics Beijing China (GRID:grid.43555.32) (ISNI:***)

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 describe the evolution laws of dynamic information. These four kinds of evolution equations are of the same mathematical type. They show in unison when information transmits in coordinate space outside the systems 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, and 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. When space noise can be neglected, an information wave will appear. If we only consider the information change inside the systems, dynamic information evolution equations reduce to information equations corresponding to the dynamic equations which describe evolution laws of the above dynamic systems. This reveals that the evolution laws of respective dynamic systems can be described by information equations in a unified fashion. Hence, the evolution processes of these dynamic systems can be abstracted as the evolution processes of information. Furthermore, we present the formulas for information flow, information dissipation rate, and entropy production rate. We prove that the information production probably emerges in a dynamic system with internal attractive interaction between the elements, and derive a formula for this information production

关键词： dynamic information evolution equation informationization of dynamic equation information wave information flow and force information dissipation and production degradation and evolution

On the fundamental equation of nonequilibrium statistical physics—Nonequilibrium entropy evolution equation and the formula for entropy production rate

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Science china(physics,Mechanics & Astronomy) 2010年第12期53卷 2194-2215页

作者： xing XiuSan Department of physics, beijing institute of technology, beijing 100081, china beijing institute of technology Department of Physics Beijing China (GRID:grid.43555.32) (ISNI:***)

In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or anothe

关键词： stochastic velocity type’s Langevin equation in 6N dimensional phase space drift-diffusion duality nonequilibrium entropy evolution equation entropy diffusion formula for entropy production rate entropy change from internal interaction a

NONEQUILIBRIUM STATISTICAL FOUNDATION OF FATIGUE FRACTURE

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Acta Mechanica Sinica 1990年第1期6卷 35-44页

作者： xing Xiusan, Department of applied physics, beijing institute of technology, beijing, 100081, china Department of applied physics Beijing Institute of Technology Beijing China

The physical foundation of statistical law of fatigue fracture is discussed. The universal forms of the microcrack growth rate, fluctuation growth coefficient and distribution function and fatigue life distribution fu... 详细信息

关键词： microcrack evolution equation microscopic mechanism microcrack distribution function fatigue life distribution function

Void damage model and service life prediction for solid high polymer

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Chinese Science Bulletin 2001年第21期46卷 1842-1845页

作者： SHEN TingfangDepartment of applied physics, beijing institute of technology, beijing 100081, china Department of applied physics Beijing Institute of Technology Beijing China

Based on the analysis of three void damage variety models, this note presents (i) a method that regards the void content as a damage variation of the grain and (ii) a geometric model for micro-unit of void damage. Equations of the void damage variety containing void content are analyzed. This work is focused on the measurement of internal damage level and the damage variety estimation is directly related to the life predication in the practical engineering applications. Nowadays, the critical service life of the solid grain/polymers is usually presumed at domestic and international level. The strength or strain reduction of 20% or the stabilizer consumption of 50% is generally regarded as a critical storage life of the solid grain/polymers, and the service life is predicted by the extrapolation method on An-henius formula. The applications, however, show that the above method is unreliable and has significant errors. With the aid of the discontiguous automatic measuring device of real time volume

关键词： void content void damage thermal aging service life damage mechanics.

Oscillatory periodic solutions of differential-delay equations with multiple lags

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Chinese Science Bulletin 1997年第6期42卷 444-447页

作者： GE WeigaoDepartment of applied Mathematics, beijing institute of technology, beijing 100081, china Department of applied Mathematics Beijing Institute of Technology Beijing China

BASED on the Nussbaum’s results, we studied in ref. [2] the conditions for the existence of oscillatory periodic solutions to the differential-delay equations (DDEs)

关键词： differential-delay equation periodic solution multiple lags.

Lie symmetry and conservation law of Birkhoffian system

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Chinese Science Bulletin 1999年第4期44卷 318-320页

作者： MEI FengxiangDepartment of applied Mechanics , beijing institute of technology, beijing 100081, china Department of applied Mechanics Beijing Institute of Technology Beijing China

The Lie symmetry of Birkhoffian system was studied, the condition under which the system admits the one-parameter Lie group of transformation with infinitesimal generator was given, and the structural equation and the... 详细信息

关键词： symmetry conservation law Birknoffian system.

Non-Noether conserved quantity for differential equations of motion in the phase space

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Chinese Science Bulletin 2002年第24期47卷 2049-2050页

作者： MEI FengxiangDepartment of applied Mechanics, beijing institute of technology, beijing 100081, china Department of applied Mechanics Beijing Institute of Technology Beijing China

A non-Noether conserved quantity for the differential equations of motion of mechanical systems in the phase space is studied. The differential equations of motion of the systems are established and the determining equations of Lie symmetry are given. An existence theorem of non-Noether conserved quantity is obtained. An example is given to illustrate the application of the result.

关键词： mechanical system phase space non-Noether conserved quantity.

Accuracy of Lax-Wendroff scheme for discontinuous solutions of convection equations

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Chinese Science Bulletin 1997年第24期42卷 2047-2051页

作者： DING LijuanDepartment of applied Mathematics, beijing institute of technology, beijing 100081, china Department of applied Mathematics Beijing Institute of Technology Beijing China

IT is known from Brenner, Thomee and Wahlbin that the well-known second-order Lax-Wendroff scheme is stable in L^2, but unstable in L^p, p≠2. Generally speaking, if the initialdata is smooth enough and if a difference scheme, which is stable in L^p for some p, has orderof accuracy μ, then we can expect that the solution of the difference scheme converges to thesolution of the differential equation at the rate of order μ in L^p. But for discontinuous solu-tions, which are essential to hyperbolic equations, the above expectation is not true. Error es-timates for discontinuous solutions not only have theoretical meaning, but also practical value.

关键词： Lax-Wendroff scheme modlfled equation discontinuous solutions error estimate.

ON THE EXISTENCE OF SOLUTIONS TO A TYPE OF NONLINEAR DIFFERENTIAL-ITERATIVE EQUATIONS

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Chinese Annals of Mathematics,Series B 2000年第2期21卷 217-224页

作者： GE WEIGAO(Department of applied Mathematics, beijing institute of technology, beijing 100081, china.) LI CUIZHE(Department of applied Mathematics, beijing institute of technology, beijing 100081, china.) YU YUANHONG(Inditute of applied Mathematics, Acad Department of applied Mathematics Beijing Institute of Technology Beijing 100081 China institute of applied Mathematics Academia Sinica Beijing 100080 China

Under the assumption that h(z) is strictly monotone the existence of solutions to a type of nonlinear differential-iterative equations in the form of x’(t) = g(x(t)) -h(x(x(t))) is discussed according to the behavior... 详细信息

关键词： Differential-iterative equation Quasi-isoclinic curve Fixed point