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In this paper, the author presents an overview on his own research works. In recent ten years, we extended the present static statistical information theory to dynamic processes and established a dynamic statistical information theory whose core is the dynamic information evolution equation describing the evolution law of dynamic information. Starting from the idea that the state variable probability density evolution equations of the stochastic dynamic system, the classical and quantum nonequilibrium statistical physical systems obeying stochastic law and the electrodynamic system obeying decterministic law can be regarded as their information symbol evolution equations and the definitions of dynamic information and dynamic entropy, we derived the evolution equations of dynamic information and dynamic entropy that express the evolution laws of dynamic information. These show that for the dynamic systems obeying a stochastic law, 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. For the dynamic systems obeying the deterministic law, the evolution equations of dynamic information and dynamic entropy are the same mathematical type as the former except that dynamic information (entropy) density only has drift in state variable space inside the systems. Information and entropy have been connected with the state and change law of the system. Information diffusion and information dissipation occur at the same time. When the space noise can be neglected, information wave will appear. If we only consider the information change inside the systems, the dynamic information evolution equations reduce to information equations corresponding to the dynamic equations which express evolution laws for the above dynamic systems. This reveals that the evolution laws of the respective dynamic systems can be expressed by information equations in a unified fashion. Furthermore, we have presented the formulas for drift and diffusion information flow, information dissipation rate, and entropy production rate and a unified information expression for degradation and self-organizing evolution. Obtained the dynamic mutual information and dynamic channel capacity reflecting the dynamic dissipative character in transmission process, in when in the limiting case the ratio of channel length to signal transmission rate approaches zero, reduces itself to the present static mutual information and static channel capacity. All these new theoritical formulas and results are derived from the dynamic information evolution equation.
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Keywords:
- dynamic information evolution equation /
- information wave /
- information flow /
- dynamic channel capacity
[1] Cover T M, Thomas J A 1991 Elements of Information Theory (New York: John Wiley and Sons)
[2] Zhu X L 2000 Fundamentals of Applied Information Theory (Beijing: Tsinghua University Press) (in Chinese) [朱雪龙 2000 应用信息论基础 (北京:清华大学出版社)]
[3] Zhong Y X 1996 Principles of Information Science (Beijing: Beijing University of Posts and Telecommunications Press) (in Chinese) [钟义信 1996 信息科学原理 (北京:北京邮电大学出版社)]
[4] Wiener N 1948 Cybernetics (Cambridge: MIT Press)
[5] Hofkirchner W 1996 The Quest for a Unified Theory of Information (Amsterdam: Gordom and Breach Publishers)
[6] Xing X S 2004 Trans. Beijing Inst. Technol. 24 1 (in Chinese) [邢修三 2004 北京理工大学学报 24 1]
[7] Xing X S 2004 Acta Phys. Sin. 53 2852 (in Chinese) [邢修三 2004 53 2852]
[8] Xing X S 2006 Sci. China G 49 1
[9] Xing X S 2010 Sci. China: Phys. Mech. Astron. 53 607
[10] Xing X S 2001 Sci. China A 44 1331
[11] Yang Z R 2007 Quantum Statistical Physics (Beijing: Higher Education Press) (in Chinese) [杨展如 2007 量子统计物理 (北京: 高等教育出版社)]
[12] Xing X S 1996 Sci. China A 39 1193
[13] Xing X S 1998 Int. J. Mod. Phys. B 12 2005
[14] Xing X S 2010 Sci. China: Phys. Mech. Astron. 53 2194
[15] Xing X S 2003 Acta Phys. Sin. 52 2969 (in Chinese) [邢修三 2003 52 2969]
[16] Frieden B R 1998 Physics from Fisher Information (Cambridge: Cambridge University Press)
[17] Haken H 1983 Synergetics (Berlin: Springer Verlag)
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[1] Cover T M, Thomas J A 1991 Elements of Information Theory (New York: John Wiley and Sons)
[2] Zhu X L 2000 Fundamentals of Applied Information Theory (Beijing: Tsinghua University Press) (in Chinese) [朱雪龙 2000 应用信息论基础 (北京:清华大学出版社)]
[3] Zhong Y X 1996 Principles of Information Science (Beijing: Beijing University of Posts and Telecommunications Press) (in Chinese) [钟义信 1996 信息科学原理 (北京:北京邮电大学出版社)]
[4] Wiener N 1948 Cybernetics (Cambridge: MIT Press)
[5] Hofkirchner W 1996 The Quest for a Unified Theory of Information (Amsterdam: Gordom and Breach Publishers)
[6] Xing X S 2004 Trans. Beijing Inst. Technol. 24 1 (in Chinese) [邢修三 2004 北京理工大学学报 24 1]
[7] Xing X S 2004 Acta Phys. Sin. 53 2852 (in Chinese) [邢修三 2004 53 2852]
[8] Xing X S 2006 Sci. China G 49 1
[9] Xing X S 2010 Sci. China: Phys. Mech. Astron. 53 607
[10] Xing X S 2001 Sci. China A 44 1331
[11] Yang Z R 2007 Quantum Statistical Physics (Beijing: Higher Education Press) (in Chinese) [杨展如 2007 量子统计物理 (北京: 高等教育出版社)]
[12] Xing X S 1996 Sci. China A 39 1193
[13] Xing X S 1998 Int. J. Mod. Phys. B 12 2005
[14] Xing X S 2010 Sci. China: Phys. Mech. Astron. 53 2194
[15] Xing X S 2003 Acta Phys. Sin. 52 2969 (in Chinese) [邢修三 2003 52 2969]
[16] Frieden B R 1998 Physics from Fisher Information (Cambridge: Cambridge University Press)
[17] Haken H 1983 Synergetics (Berlin: Springer Verlag)
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