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

Nonequilibrium statistical information theory

In t his paper, we propose a nonequilibrium statistical information theory, whose ke rnel is information(entropy) evolution equation describing information evolution law. A nonlinear evolution equation of Shannon information (entropy) is derived . The statistical physical information is introduced and its nonlinear evolution equation is derived. Both of these two information (entropy) evolution equatio ns show that the temporal change rate of statistical information (entropy) densi t y originates together from their drift, diffusion and dissipation (production) i n coodinate space (and state variable space). The expressions of drift informati on flow and diffusion information flow, the concise formulas of statistical entr opy production rate and statistical information dissipation are given. The stati stical information dissipation (or increase) rate being equal to its statistical entropy production (or decrease) rate of the dynamic system, the information di ffusion and information dissipation occuring at the same time are proved. The d ynamic mutual information and dynamic channel capacity reflecting the dynamic di ssipative character in transmission process is presented. The similarities and dissimilarities between Shannon information (entropy),its evolution equation an d physical information (entropy),its evolution equation are discussed.