On dynamic information theory

Abstract

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.